Sl;
Congrats on locating and repairing, and thanks for following up with a report of findings.
Be aware...if "oil/grease buildup on both electrical contacts" is enough to prevent electrical contact, the spring preload of push-on terminal (which
should be present!) must not have been very good, because by design, pushing on terminals should cut through oxidation and surface contamination to allow contact of clean metal surfaces. This means after cleaning terminals of switch, you may want to (at the very least) squeeze terminals to restore some preload, and (at the very most) replace crimps with new! ...and of course: Apply ACZP!
Suggested reading:
http://www.sw-em.com/voltage_drop_in...sh_on_terminal
Finally, you may have restored Brake Light function, but you haven't removed any of the known weaknesses. Please keep upgrading in mind as a future safety and reliability improving option!
Cheers