[Porboynz]

Re the battery, if a single cell has gone bad you will struggle to retain 12V after charging. Sometimes if an older battery is allowed to discharge (eg interior light left on) a single cell can go into reverse polarity when recharged if its internal resistance is different to the others. A lead acid battery has 6 cells each with a nominal voltage of 2.105V = 12.63V. If one cell is dead then 5 x 2.105 = 10.525V. Your 11.25V suggests one cell is on the way out if this is what it measures disconnected a few hours after charging with a known good battery charger. The new smart chargers are great and will often bring a dead flat battery back to life. I remember changing British car electrics from positive earth to negative earth to suit a new "modern" radio cassette player, we had to flash the generator by quickly closing the regulator relay contacts before starting. I do not recall any issues with starter motors trying to run in reverse, but that was a long time ago. Alternators with internal regulators are a bit fussy about the warning light specs, there a few posts about this and the need to add shunt resistors or change the bulb to get the alternator to charge correctly, maybe this is something to look at? I do not advise feeding a raw 12V to the blue wire, that warning light bulb has resistance to limit current and drops the voltage down from a full 12V for a reason. Now that you have a good battery in place its time to get back to basics and measure the voltages at idle with the warning light on and again at 2000 rpm with the warning light hopefully out to check correct alternator performance. You can also get auto multimeters with shunt current capability to check how much current your alternator can pump out. The shunt looks like a strip of metal, the meter connects to terminals at each end and calculates the current by the small voltage drop across the low resistance metal shunt.