[Bobcat]

Dan ... the heater switch on mine is doing what yours is . Looks like Lucas strikes again . Probably a defective switch . I was able to move mine around until I found a sweet spot where the fan cut off ... but if I hit a good bump , it comes back on . On my Winter list to replace .
Yes , for your brake lights to come on , you need hydraulic pressure on the switch to activate it ... i.e. master cylinder filled and system bled .
Electrical gremlins can be a bear to track down and not one of my favorite things to do .... and I was a EE in a previous life .
Have fun??