Aaron, since you want to change the property on a Thing, you would have to bind the button output to 'set' service on that Thing. Try binding Radio Button's 'SelectedValue' to the 'SetProperties' service on your Thing. Once you add 'SetProperties', you can expand that and bind it directly to your specific Boolean property. Also, do remember to bind the 'SelectionChanged' event on the Radio Button to the 'SetProperties' service as that will trigger the actual property changes.
Thank-you Aanjan, this was helpful.
For others reference;
In the mashup composer area, select the Data tab on the rights hand side, add "yourThing".
Then select yourThing, and add "Set Properties" Service
1. Drag the Radio Button widget to Mashup
2. Mouse over the widget upper left corner arrow, click on the "Configure Bindings"
3. Goto Properties "Selected Value", click on "Binding Targets", and choose the local or remote target
4. On the "Add Data Binding" pop-up, "Data" List, navigate to /yourThing/Set Properties and select "yourProperty"
5. Return to "Configure Bindings" area, goto Events "SelectedChanged", click on "Triggered Services"
6. On the "Add Services" pop-up, "Data Services" List, navigate to /yourThing and select "Set Properties"