Lee, the part that comes off the area that attaches to the ball is smaller in diameter than the rest.  It slides into the rest and pushed rod into a piston on the brake master cylinder.  If you poo it with a mallet or block of wood, does it compress into the rest of the trailer?

Within it there is likely a break master cylinder (unless it has been removed). One clue to finding it would be to follow the break line. 

An underside pic might also help. 

The shock on the top is what helps damper the movement at the end of the stroke. 

I will say, more than likely your best bet will be to measure the distance between the two horizontal bolts on the rear of it under that shock.  Those hold it to the trailer.  Go to etrailer or pacific trailer and find a whole new bolt one surge brake actuator with the same bolt patter and replace it. 

I say this because chances are the brake master cylinder might be all rusted out and full of crud.  The only way to know, though is to take out bolts and pull the tongue part out.  Maybe they made them better back then that the news ones – most things were made better back in the ole days.  My UFP brake master cylinder on my other boat’s trailer died at year 15 of its life. 

Also, I am newer to theses PCM 351 as have only had my 85 SN2001 for about 5 years.  I am on the other side of Nashville.  I may not have lots of knowledge to offer as you get that Fish seaworthy again, but if you need an extra set of hands send me a pm.

Richard