problem #1- your ecm has stored trouble code 16.....your battery sounds like junk.....battery tenders do not sufficiently charge batteries.....battery with cracked/broken terminal should be replaced immediately. then test charging system for proper output. think i covered all your ailments.
problem #2-the little mechanism as you stated is the front brake light switch. common nissin part. the H-D/Buell part # is Y0820.9 suzuki part # is 57460-17C01 kawasaki part # is 98005-031 test by removing the 2 wires and with key and run switch on, jump the wires. brake light illuminates? bad switch. does not illuminate? something else awry.