You can lead a horse to water........ 4 pages over 3 days to check if an alternator is charging. It takes under a minute to check 2 conditions. Is it exciting and if so is it sending 13.7+ to the battery
You took the neg lead off when running to check if charging ( bad idea, hard on the internal regulator )
You mention that the car is "hot wired", messing with this wiring may have something to do with your charging problem ( bad idea )
Your pic shows the 12v ground wire from the battery to the alternator bracket is off and dangling ( bad also )
Longroof has advised you "excite" the alternator by jumping 12v to the brown wire then check the output ( this takes less than 30 seconds and a 6" piece of wire)
You can see by the wiring ( 2 heavy red leads ) that Olds ties in the power from the alternator to the lug on the starter and back to the battery for charging ( chev runs a lead from the alt to the battery direct ). Longroof and others have suggested you bypass / add to this additional wire to your system and see if its now charging. ( another lest try this to see if it works 30 seconds fix ).
Try any of these excellent suggestions and report back. Or as mentioned above take it off and take it to just about any parts place to be tested for FREE.
I get you are on a budget but you have been given excellent information here and none of it is very expensive.
4 pages over 3 days due to me trying to cross every possible problem off the list. Lets also keep in mind sunday things close early, and a disabled person like myself requires more rest than the average person.
And 2 Conditions to test for yes, but more than one method for testing exists keep in mind. Please be patient, cause this is giving me a headache too(although in hindsight it shouldnt lol)
As i haven't gotten anything in the 13v range so far, and the 12v ground wire from the battery was never attached when i first bought the car, where would this ground wire on the alternator specifically be attached, if you dont me asking?
I will try jumping the brown wire after wiring the alternator directly to the battery first.