Wow Jules!
Ya' all move fast! I remember posts from Northern Peru' just a couple weeks ago. Weren't you guys awaiting parts up there? That is blazing fast!
Hope you get the chance to explore some of the interior of Peru' and Bolivia, N. Argentina, S. Chile, just so much to see and do. But if the bikes causing trouble, I know how that can ruin the whole trip.
Seizing brakes could be a number of things. I ain't no BMW expert but have owned a few and ridden many others. I do my own maintenance on Jap bikes no problem .... but not much to do, as they rarely fail!
Do you have ABS? IIRC, BMW claim it's impossible for the ABS to cause this, probably correct. But I would clean and check all connections anyway. Check all fuses, computers, whatever. Make sure system is operating correctly.
Could be water in the system. Add heat = expansion of water and seized brakes. I'm assuming you've flushed pints of brake fluid though already? This would be job one. And make sure it's the right type of brake fluid.
(DOT 3 or 4, or maybe 5 - I'd guess?)
I'm sure you've cleaned the Caliper pistons already? This is big in the UK, but in 30 years of riding in mostly California, I've never done it and never had corrosion!
Make sure the caliper pistons are operating in and out freely and that seals look OK, not torn or out of position.
Could also be a failed Master Cylinder. (Hope not!) Are you able to "bleed" the brakes OK? If not, could be bad Master Cyl. but unlikely.
Make certain the pads are seated in the Caliper correctly with spring clips set correctly so pads do not drag and tabs on pads are right way round.
(yes, I've seen folks put them in upside down!)
One possible move is to remove the calipers, pull brake line off and drain and flush completely with fresh brake fluid. Make sure all water and old fluid are flushed out. Then pump fresh brake fluid through disconnected brake lines. Then hook it all back up, add more fresh fluid and pump through another pint to remove any air.
Pro mechanics use a vacuum ... forgot how that works, I've never done it, but seen it done. Most pro's use this method, doubt they will have that in
Argentina.
Brake fluid is hydroscopic (attracts moisture), needs to be changed every 6 months, especially if riding in humidity and high temps or lots of rain.
Seems your old Bimmer has been a right Pain so far ... was it worn out before you started? Or just now deciding to give up on you? Shame!
Any case, best of luck. There are a few Mec's around down there, but IIRC, there may be some MC guys in the nearby towns, not in Usuhaia. (perhaps Rio Gallegos, or something? Can't recall)
Hey, no worries, Helge Pederson fabricated a whole new drive shaft while down there, of course it broke again shortly after!
Cheers, don't give up!
Mc D