Problem fixed !
It turned out to be a problem with the combination switch. I disassembled the switch and found carbonized (?) material (probably the contact grease) between the center and left contacts, which formed a ~10 ohm resistor. It was hard and I had to cut it out with an Xacto knife.
Sorry, I forgot to take pictures.
Thanks to SBM for the link to the schematics.
In case this happens to any of you, the fix cost $0.00. If you're not brave enough to open up the switch, you can buy a new one for $80 MSRP.