I found my first restoration project (a Healy 3000) in a guys leaking garage, it had been sitting that way for about 9 years. Paid $1500 for a complete car. Three YEARS later had it on the road again, after a ground up resto.
Those funny "pistons" you guys refer to are known as "dashpots",
oil filled slightly in the center chamber to help smooth acceleration and deceleration.
If you decide to take on that Triumph may the force be with you, and may the Lucas gremlins smile upon you.
I never got to see them, just the fuses they liked to blow, a lot of them.