At the request of @skipcurt I'm posting how I made a remote switch for my garage door opener on my ST1300. Everything would be identical on the ST1100, or any other bike for that matter, except to my knowledge the ST1100's fairing pocket lacks the convenient drain hole at the bottom which I used to route the wire.
So I'm going to write up what I did on my bike, but I already have an easier solution resulting from switches with prewired connectors that I either missed or weren't available when I went searching a year ago. You all benefit.
Parts:
So I mentor a high school robotics team where my son was a student member. This has given me access to tools and supplies I might not have had otherwise. Hence, ready access to a short length of wire, connectors and crimper. But I tell you now, that these connectors, tools and supplies make for projects and add-ons that are so much better than the usual butt connections and wire taps. They're cleaner, more reliable and can be disconnected when you have to perform maintenance that might otherwise have messed up your project. These JST connectors are suited for low power applications. For most applications, like connecting devices to the quartet harness, I used Hitachi connectors also available in a kit from Amazon, but those would be severe overkill for this application.
My garage door opener is a Liftmaster. Third party replacements are readily available on Amazon for a very low price.
Gate1Access 971LM Replacement Liftmaster Sears Craftsman One Button RED/Orange Program Button Security + Remote 390mhz Transmitter 2 Pack

This is a very affordable JST connector kit with crimper (for low voltage/low current applications)
QLOUNI 560Pcs 2.54mm Pitch 2 3 4 5 Pin with SN-2 Crimping Tools Dupont JST SM 2 3 4 5 Pin Male/Female Plug Housing Male/Female Pin Header Crimp Terminals Connector Kit

This would be my current preferred momentary switch with included mounting plate and in-line connector based on ebay description (I have not personally used this specific product!)
Push Momentary Switch Motorcycle Handlebar Screw Mount Waterproof Thumb Button

Procedure:
Open the remote case to access the circuit board inside. Locate the momentary switch on the circuit board and determine which terminals close the circuit to activate the remote. You can use a paperclip or the tip of a screwdriver to determine which activate the garage door opener.
Decide how you'd like to pass the wire into the case. You can drill a hole into it on the same side of the board as the switch, or as I did, I use an existing hole on the backside and drilled a hole through the circuit board to get to the switch. These remotes have very simple circuit boards and should present a lot of unused space that would be completely unaffected by drilling that hole.
Modified and unmodified remotes.


Leads bridging the momentary switch to operate the remote.

JST female connector

Modified remote with remaining parts - switch, cable, JST male connector and terminals, protective boot, lock ring and mounting plate. Missing is heat shrink tubing to protect connector.

Here the switch is mounted to a RAM mount, RAM-B-309-2U. A switch mount with a shorter leg would only require mounting using one bolt rather than two as I did.

I routed the cable from the switch along the left handlebar and under the body panels to the front of the left fairing pocket. I also passed the wire from the remote through the hole in the bottom of the pocket and attached the remote to the wall of the pocket with a 3M Command Performance strip. Why? Well, I'm going to have to replace the battery at some point. Why make it hard on myself by using a more permanent adhesive. You do you.
By using that connector you can disconnect it when it comes time to remove the bodywork for maintenance without ripping out the wiring all the way back to the handlebar.

If I were to do this again, I'd likely go for one of the many similar switch sets which I've seen on ebay since. A lot of them include the inline connector already and have a shorter leg for attaching to something on the bars. Why does mine have room for two switches? That's where the latching switch for my yet to be sourced driving lights will go.
You asked @skipcurt
And you're welcome.
So I'm going to write up what I did on my bike, but I already have an easier solution resulting from switches with prewired connectors that I either missed or weren't available when I went searching a year ago. You all benefit.
Parts:
- Replacement remote for YOUR garage door opener manufacturer - Amazon
- waterproof momentary switch with mounting plate and attached wire - ebay
- 2-pin connectors - JST style or equivalent - Amazon
- two conductor wire - 18 to 22 gauge (smaller wire feeds more easily into the remote housing) - wherever
- 3M Command Strip or 3M VHB tape
- heat shrink tubing (1/4" ?)
- twist drill
- soldering iron and solder
So I mentor a high school robotics team where my son was a student member. This has given me access to tools and supplies I might not have had otherwise. Hence, ready access to a short length of wire, connectors and crimper. But I tell you now, that these connectors, tools and supplies make for projects and add-ons that are so much better than the usual butt connections and wire taps. They're cleaner, more reliable and can be disconnected when you have to perform maintenance that might otherwise have messed up your project. These JST connectors are suited for low power applications. For most applications, like connecting devices to the quartet harness, I used Hitachi connectors also available in a kit from Amazon, but those would be severe overkill for this application.
My garage door opener is a Liftmaster. Third party replacements are readily available on Amazon for a very low price.
Gate1Access 971LM Replacement Liftmaster Sears Craftsman One Button RED/Orange Program Button Security + Remote 390mhz Transmitter 2 Pack

This is a very affordable JST connector kit with crimper (for low voltage/low current applications)
QLOUNI 560Pcs 2.54mm Pitch 2 3 4 5 Pin with SN-2 Crimping Tools Dupont JST SM 2 3 4 5 Pin Male/Female Plug Housing Male/Female Pin Header Crimp Terminals Connector Kit

This would be my current preferred momentary switch with included mounting plate and in-line connector based on ebay description (I have not personally used this specific product!)
Push Momentary Switch Motorcycle Handlebar Screw Mount Waterproof Thumb Button

Procedure:
Open the remote case to access the circuit board inside. Locate the momentary switch on the circuit board and determine which terminals close the circuit to activate the remote. You can use a paperclip or the tip of a screwdriver to determine which activate the garage door opener.
Decide how you'd like to pass the wire into the case. You can drill a hole into it on the same side of the board as the switch, or as I did, I use an existing hole on the backside and drilled a hole through the circuit board to get to the switch. These remotes have very simple circuit boards and should present a lot of unused space that would be completely unaffected by drilling that hole.
Modified and unmodified remotes.


Leads bridging the momentary switch to operate the remote.

JST female connector

Modified remote with remaining parts - switch, cable, JST male connector and terminals, protective boot, lock ring and mounting plate. Missing is heat shrink tubing to protect connector.

Here the switch is mounted to a RAM mount, RAM-B-309-2U. A switch mount with a shorter leg would only require mounting using one bolt rather than two as I did.

I routed the cable from the switch along the left handlebar and under the body panels to the front of the left fairing pocket. I also passed the wire from the remote through the hole in the bottom of the pocket and attached the remote to the wall of the pocket with a 3M Command Performance strip. Why? Well, I'm going to have to replace the battery at some point. Why make it hard on myself by using a more permanent adhesive. You do you.
By using that connector you can disconnect it when it comes time to remove the bodywork for maintenance without ripping out the wiring all the way back to the handlebar.

If I were to do this again, I'd likely go for one of the many similar switch sets which I've seen on ebay since. A lot of them include the inline connector already and have a shorter leg for attaching to something on the bars. Why does mine have room for two switches? That's where the latching switch for my yet to be sourced driving lights will go.
You asked @skipcurt