Help with an electrical problem please.

[Pills]

Hi to all. This is my first post on this forum (even though long time lurker) so allow me to introduce myself.

My name is Chris, and I am the owner of a RAM cobra with a serious electrical fault.

This is some background: Have had a problem with a flat battery, so replaced it, as I could not tell how old the original was. Have since driven the car once or twice weekly and the battery has not been holding its charge. Hmmmm out comes the multimeter.

Motor not running Battery showing 12.45v
Motor running Battery showing 12.32v ??

At the alternator with motor running, showing no voltage output???
Now the funny thing is whilst I was checking the alternator and looking for a better ground, the thermo fan kicks in and the Multimeter now reads 13.65v.

So unless I am stationary for long periods or driving like I stole it (which I never do) then I am not getting any charge back to the Battery.

I don't have a lot of electrical knowledge, so my question is, should I be looking for an electrical short circuit somewhere, or perhaps the thermofan relay for a fault.
I should also mention that the thermo fan relay draws its power direct from the alternator, which I thought is unusual.

Whilst driving the car all this time, I have had no problems with warning lights etc, except for this last weekend when my check engine light came on, but by the time I returned home had gone away.I suspect this was from a low battery not being charged.

Any hints as to help narrow the search for the problem down would be greatly appreciated.

Cheers Chris.