Re: How can you tell what model and make of stringer drive you have?
Good times - that thing is a monster! Hope the stringer doesn't give you too much trouble.
You're definitely electric shift, I can see the cables in the second photo. Your exhaust housing is a little different than mine, so probably a '70 or '71. You can find the serial number on the drive and figure it out with a quick Google search. NWRedneck has a great post of general information on the stringers
here.
Your tilt motor is also disconnected from the looks of the first photo. You may want to service that tilt motor and gears while you've got the boot apart. The boot should be pretty easy to replace once you pull the outdrive. There's a clamp on the inside of the boot at the intermediate housing, and then the screws around the transom. Count your screw heads and commence to orderin'.
Can't wait to see some pictures inside the boat.