The electric part would be in the trim, yes?
Nope. Electric motors do run the tilt (motor at the back by the quadrant gear that lifts the drive up and down) and trim (if you have it will be at the front of the engine). But the "electric" part that gives it it's name is the shift. Most drives are shifted by a mechanical process now, but the old Stringers used electricity to power a coil/magnet and that's what put the lower unit into gear.
Is Stringer a name brand or a model type?
OMC is the brand. Electric Shift Stringer is the type of drive. See below for the model:
For clarification, I own a 1975 AMC Slickcraft with an OMC 235 inboard and what is begining to appear as a Stringer drive
Not just appearing
It's an Electric Shift Stringer. Post number 4, I gave you a tip on how to find the model number. The engine on a '75 235HP should be a Ford 351 and the model number should be something like 990240AST. The Stringer Info link in my signature will have some information on the drive, but you will want a good manual for it.
Where do I find a manual on the Stringer drive?
The link in post 1 should have the OEM shop manuals I believe. You can also find them on eBay.
I have the large diaphragm in the back.
Stringer drive good or bad? I am a mechanic so doing the work isn't a problem. Need to know life expectancy and tips to keep it running after 40 years.
That diaphragm is the transom seal or transom boot. Make sure it's in good shape. They can last a very long time, but when they let go that's a big hole for water to come in.
The Stringer is not a bad drive at all. It's old like Scott said, and some parts are getting hard to find. I've kept mine going for six years or so for not too much money, and the inline 6 in mine is original to the boat (drive is collected parts). It'll want attention in the garage, and you do have to keep an eye on maintenance. But there's no reason it shouldn't run for a very long time.