Doc here,
imp:
First, without all the documentation in front of me..your troubleshoot is hard to follow , BUT sounds logical to me..
The first thing to do, is go back to that ground..Take your meter, and Calibrate it on Ohms scale, Short the probes together, on R X 1, for "000" This takes the resistance Factor out of the probes..
IF you do that and Still get 0.2 ohms to ground, try some fresh battery's in the meter..IF you STILL get the 0.2 reading, Burnish the metal bare, Install a star washer, a lock washer, and Tech screw..
IF you Still get a 0.2..run a ground wire DIRECT to the battery..(and consider a ground buss install, you may have different potentials Throughout the body/frame/engine which will come back on you later..)
NEXT , I believe the Cruise control MAY NOT be compatible with LED tail/Brake lamps..OR it has a MAJOR malfunction..( this is more likely) Sooo, your faced with two choices..Pull the CC completely out..box it up and send it back defective..OR you Could get a DUEL brake lamp switch..Which , other than leakage, IF the CC will work, MAY solve ALL the problems.
The Duel brake lamp switch would be identical to a single switch EXCEPT it has Four sets of contacts..two for Brake lamps (Hot and Lamps) and Two for Cruise Control (hot and disconnect) Both would be isolated circuits from one another..
IF you can't find a Duel brake lamp switch for your application, you Can use a relay and achieve the same result..
Just from what you have posted, and without seeing the schematic, This is what I think is what may be happening..There is a BAD transistor or Linear OP amp in the cruise control that has a minor reverse bias leakage (small amount of voltage/current at the base of the semiconductor) that shouldn't be there.
Akin to one bad diode on an alternator..it still charges, but goes dead over night because it (the bad diode) has a reverse bias and imposes a load on the battery just sitting..
NOW, in a normal setup (incandescent lamps) that voltage/current would not effect a thing..because it couldn't be used as a source of power to another circuit..In your case, it IS using current because the LED only asks for a Very small amount of current to operate..OK, This in turn starts a "Chain" , that may be ENOUGH current to forward bias the gate on the semiconductor in the cruise control Brake lamp connection (the Disconnect part of the CC Circuit) and the CC THINKS the brakes are on..(because the lights are on..) and automatically disconnects the CC from engaging..Hence..it doesn't work when switched on..
Do you Follow the logic path? Hope so..
Anyway, I think the Cure is a duel Isolated Brakelamp switch (or relay if not doable) second only to sending the CC unit back defective and trying another..(and this may not be the cure..that small voltage may be typical on all their units..)
Doc
imp: