Hi Richard
welcome to pinside. I was hoping "a proud owner of 4 Millions BC" helps on Your problem(s). It was some 40 years back in time when I played that pin - I do not remember the rules. I can offer help with reading the schematics - but You must explain in detail "how does the Tar-Pit works in an fully running pin".
See https://www.ipdb.org/showpic.pl?id=935&picno=52455&zoom=1 - I see a gate before the entrance to the Tar-Pit. I assume it can be closed - no ball in the alley. You then open the gate - a ball rolls in - is the ball (?) immediately locked after the gate ? Does the gate then close - means "always maximum ONE ball in the alley" ? I believe to see the light "1000 when lit, advances ball in Tar-Pit" - and the mushroom bumper above. Hitting the mushroom bumper makes the ONE ball (what is the maximum of balls ?) roll down a bit - then mechanically stopped. Hitting the mushroom bumper again makes the ball roll down once more - then mechanically stopped. Hitting the mushroom bumper again makes the ball roll down and rolling out of the alley. Write about "how it works". Have You checked for "mechanical problem (locking)" ? Greetings Rolf

Hi jeffc
shall I write it or should I not (?) - jeffc: May want to wait with making an video - until the OP (Quercus22, Richard) answers (?).
Looking through ipdb - I found: https://www.ipdb.org/files/935/Bally_1971_Four_Million_B_C_Instruction_Manual.pdf --- and in there are (most or all) answers to my questions on "functionality of Tar-Pit". Greetings Rolf

Hi jeffc
thanks for the video. Yes - only ONE ball in the Tar-Pit-Alley. Here https://www.ipdb.org/showpic.pl?id=935&picno=32775 I believe to see the unit --- if Quercus22, Richard writes again - You then together may want to check "mechanics" ? Greetings Rolf

Hi jeffc
a good site: http://www.planetarypinball.com/mm5/merchant.mvc?Screen=BOOK
and then:
http://www.planetarypinball.com/reference/partsmanuals/BLY_Parts_1976/index.html#/168/
and
http://www.planetarypinball.com/reference/partsmanuals/BLY_Parts_1976/index.html#/200/
I guess these are the parts - the releasing the ball to roll down to the next halt done mechanically (?). Greetings Rolf

Hi jeffc
thanks for the excellent video - Yes, on the playfield two Half-Steps are done - similar to when the Replay-Counter steps down (when starting a new game) - TWO Half-Steps.

Hi Richard
first I thought "mechanical problem" - then I had a look at the schematics - a bit confusing so I said "maybe electrical problem" - then You and jeffc came with post-8/9 and -10 - "mechanical problem". 100% sure "only mechanical problem" ? The Bally-Page You show says "Mad World and Capersville" --- Your pin is Four Million B.C.
I show what "confuses me" - see the JPG, "encircled blue": What for is this Switch "End-Of-Stroke and switch opens" on the Tar-Pit-Gate ?
The Tar-Pit-Gate is made like a flipper-bat - when actuated and PULLING-IN - at end the EOS-Switch opens and makes to flow "just a bit Self-Hold-Current". Greetings Rolf

0Four-Million-BC-Work-02 (resized).jpg

Hi Richard
Your post-12 "presumably ... without burning the coil": Yes.
I look at the first picture in Your post-9 - Yes, maybe something has broken-off - have You looked in the bottom of the pin for the broken-off part ?
May want to try here https://pinside.com/pinball/forum/topic/the-em-seeking-parts-thread to buy an replacement-unit ?

I looked at jeffc 's linked (post-5) video - Yes, a fun pin - and the Tar-Pit has a vital role - to get Two-Ball Multiball.

I cannot help when You want to try "making You an replacement part 'stop-piece' " --- may first try "cardbord - easy to cut" - when You have the correct form: Then do it with "aluminum plate" ? Greetings Rolf