Donny,
DoT 3/4 can gel or crystallize, esp. if the car sits for long periods. If you see crud in the reservoir, the entire brake system may be contaminated. I doubt soft 'snot' would cause a front piston to hang up; there is probably crud on the caliper piston seal causing it to stick. This is an obvious safety issue; IMO you must inspect, clean and repair the system as required. At the least, you should empty the reservoir, break the connections at each wheel--and the master cylinder--and flush the system (might be a good time to replace the flex lines, too). I would use a flare nut wrench for this; most fittings on a Healey are 7/8" though IIRC there are some smaller ones on the master cyls. If you have a Harbor Freight in LV they have cheap flare nut wrench sets. I would flush first with denatured alcohol or brake cleaner, followed with copious amounts of air to dry everything. Inspect the fittings and the flare on the ends of the pipes. Any cracks or distortions on the pipe flares will cause you grief sooner or later. This would be the time to replace the switch if you still suspect it. Reconnect the lines--being careful not to cross-thread--and refill with fresh brake fluid. Remember, DoT 3/4 absorbs moisture from the air very quickly so get a new (quart or liter) bottle--and bleed the whole bottle through.
If this fixes the stuck caliper, fine. If not, you will need to pull that caliper and essentially rebuild it. If you do one, you should do the other, and the rear slaves as well.
Obviously, you can farm this job out (it will cost hundreds of dollars), or try it yourself. We all started as lousy mechanics (heck, I still am), but we kept at it. Allow yourself plenty of time to do the job, inventory the tools and parts you'll likely need and acquire them, think it through and be patient with yourself. If you have any 'mechanic' friends invite them over for a beer and subtly steer the conversation towards cars, like 'hey, I have this old Healey with brake problems, and ...'