Welcome to TRS
Does your starter motor look like this:
https://i.ebayimg.com/thumbs/images/g/CmwAAOSw1pZdXV9s/s-l300.jpg
No relay, just 1 larger cable connected
OR
This:
https://www.partsgeek.com/assets/dimage/fulln/07605847-1539359.jpg
Has relay, 1 larger cable and 1 smaller wire connected
Should be the first one, no relay on starter
So only the starter relay on the inner fender can send Battery Volts to the starter motor
On the starter relay there are 2 larger posts
One post will have battery positive cable and several other smaller wires connected, this is the Power Distribution post for the whole vehicle
The other larger post can ONLY have 1 cable connected, the one that runs to the starter motor, NO OTHER wires can be on this post
There will be 1 or 2 smaller posts on starter relay, marked "S" and "I"
The "S" post should have the wire from ignition switch connected
When is wire has 12volt the starter relay will activate, so next time starter seems to stay activated pull off this wire, before pulling battery cable, so see if that stops the starter motor
If it does then that wire is shorted to a 12volt wire some where
If it doesn't stop starter then problem is that the starter relay is locking up in the ON position, not releasing when the 12v is removed from "S" post
I am basing this off what you said in your post, about disconnecting battery post stops the starter motor BUT DOES NOT CAUSE ENGINE TO STALL
So after start up, starter stays on, and you pull battery cable off battery, engine stays running but starter stops running
If engine also stalls then there are other possibilities
If engine stalls then alternator is not working, and starter motor was probably off but its GEAR was jammed in ring gear and it couldn't be retracted, which "sounds like" starter is on, but its not, its just being spun by the engine which is not good either, lol, but different type of issue
You can test starter amp draw yourself
Disconnect Coil wire to distributor, so No Start
Put Volt meter on Battery
12.3volts to 12.8volts is a good battery, 12.2volts and under is a 6+ year old battery and time to change it
When starter is activated you should see a 2 volt drop in battery voltage, so if it was 12.5v then should drop to 10.5volts
If it drops to under 10volts then starter is drawing too many amps, or Battery is bad
But that doesn't always mean its a starter motor issue, it can be battery cables and cable to starter that are corroded inside, they don't pass the high amps well so MORE AMPS need to flow
That includes the larger Negative battery cable, not just the positive cables
When engine is running, re-test battery volts, should be 14-14.9volts just after start up
Then 13.5v-13.8v, under 14v, after 5-10minutes of idling
If so Alternator and voltage regulator are working