They are remarkably simple and bulletproof things. Carburetor, CDI with a couple mags on the flywheel, two spark plugs.
IIRC, the 80s versions should have a whizzer to indicate water flow. It should "pee" from the back of the cowl. If your model has a thermostat, it will only pee when the stat is open, so don't panic if it isn't whizzing from that tube. Run it for a while. If it doesn't start peeing, so a quick check on head temps (carefully so you don't get burned). The head should be almost too hot to touch, or you should be able to keep your fingers on it for a couple seconds depending on your heat tolerance. If you burn off your fingerprints and it's still not peeing, then you have either a water pump that isn't pumping, or a thermostat that isn't opening.
Follow the pee tube back to the block. If it meets up with a miniature thermostat housing, you have a stat. If it just attaches to a nipple on the block, you don't. I'm having trouble remembering if an 87 would have a stat, but I know my 92 did.
Don't stress about the water pump. If its pumping, it's good. They are ridiculously simple rubber vanes in a brass housing inside the lower unit right where the plate is above the prop. They do fail, and some people replace them every year to be safe, which I find equatable to changing the oil in your car ever day. I boat far more than the average person. As in, 3-4 times a day for 3 months of the year. I live on a lake in the summer, and boating is my life. Having said that, I have a 1960 Evinrude 10hp that has been in use on that lake since 1960. My grandfather bought it, my dad inherited it, I abused it, now my nephew abuses it. To the best of my knowledge, the water pump has never been replaced. To the best of my recollection, here is the rest of the fleet and their water pump history:
1968 Merc 65: Never. It went until the late 80s and dad had to replace a prop seal. He thought it would be wise to do the pump, but the bi-metal corrosion was so bad he couldn't get the bolts out to remove the lower unit. Rather than risk breaking something, he just left it alone.
1988 Merc 70: Once. Not because it had failed, but because we had the whole thing rebuilt a couple years ago.
1967 Evinrude 6: Once. It sat in storage for about 10 years and my nephew wanted to revive it. He decided to check compression while it was dry. The rubber had fused to the brass and it damaged the tips of the fins.
1992 Merc 25: Never. I have no idea how many hours were on that motor when I sold it, but it was a LOT. It sat for 3 years before I sold it and when I fired it up, it pumped fine
mid-80s Johnson 48 special: Never.
The secret is to never spin the crank unless the pump is wet. Although, my neighbor at the lake does it every year. He uncovers it in the spring and fires it up dry on the trailer for a few seconds just to be sure it runs, and I don't think he has ever replaced a pump.
Use sta-bil, don't use sta-bil, it won't matter. In this situation, I will (shocker) go along with the recommendation to use non-ethanol fuel. The rubber in that older engine will start degrading with ethanol. It won't hurt to run one or two tanks through it. It's not like the damage is done immediately, its slow, and the worth thing that will happen is it will start sloughing off flakes of rubber from the inside and clog jets. Replace the fuel lines with newer ethanol-compatible rubber, clean out the carb, now you can run ethanol fuel forever. Using sta-bil is GREAT for preserving gasoline, but many of the formulations contain ethanol. I never understood why people go to such great expense and trouble to buy ethanol-free gas, then put ethanol in it to stabilize it. Here's what I do: Run it out of gas (including the line from the tank) and tilt it down so the water runs out. Done. Stuff the boat in a field with a tarp over it and walk away. In my I/O, I don't even run it out of gas. I drive it on the trailer and turn off the key. Period. Take it home, open the block and manifold drains, and walk away. For the last 15 Springs, I put earmuffs on the inlet, turn the key, and it fires up. No sta-bil, no ethanol-free gas, nothin.
Fogging the engine (which is more or less a process of shooting a preservative in the carburetor until the motor dies) is a fine idea, but IMO it's overkill. The current 1988 70hp Merc on dad's boat has endured the same abuse I have given mine, and after 30 years it finally had enough compression loss that we rebuilt it. We're talking WOT runs to the other end of the 13-mile lake for bass fishing in the morning, a 3-4 hour lake day with lunch and skiing, then a 3-4 hour evening trolling for walleye where it idles for hours at a time. The full gamut of every possible abuse you can give it for 30 years.
One thing I always do. Before freezing weather arrives, I always drain my lower unit oil. If you developed a leak during the boating months and there is water in there, it likes to make rusty, freezy, breaky things happen. If you live where it doesn't freeze, I at least let pull the drain for a few seconds to check for water/milkshake. Nice to know that in the fall while you have time to fix it. To ensure that the drain/fill plugs aren't the cause of the leak, get new plug gaskets. They're cheap. Like a few cents cheap. I am totally in the habit of a complete drain, but if you haven't established a habit, notes are a good thing. If I do something that is outside my normal habit, I will open my calendar app and set a reminder for May 1st that says "lower unit not drained Merc 70" or something. Dad has a bunch of those little tags with wire twisties on them and he'll write down what the status is and tie it to the steering wheel.
Otherwise, pull the cord, abuse the heck out of it for 20 more years, and have fun.