Thank you Harold!
I got the inside back of the freezer off. It's a bit embarrassing that I didn't see those clips - actually, didn't think that's what they were for - every one I've ever done before had screws to remove.
There wasn't any icing up and the evaporator was mostly free of frost and ice. I poured a couple ounces of hot water across it, and some came out the drain tube into the pan down below, but a lot more came out from around the plastic thingie with the little built in p-trap. Took that and the tube out, and after a good cleaning water came through nicely. Put it all back together and everything was ok.
The next day my M-I-L says there's a lot of water on the floor below the fridge. I go back and go through it all again, but it's still all good. While I'm checking it out from the back of the fridge, the ice maker calls for water and water gushes from the bottom of the solenoid for some seconds.
OK. I have a solenoid problem. What do I do? Wait for it to call for water again? No way! I disconnect the solenoid, and cut and strip both sides about 1/4 inch from the end of an old power cord. Plug it in and tap the wires on the solenoid terminals, and the solenoid clicks on - and water shoots from where the tube to the icemaker attaches. I take the solenoid out and when I put power to it it clicks. I put the tubing in, but tightening it doesn't hold the tubing in place.
It took a while, but I finally figured out there was a maybe 1/4" piece of tubing in there. Take that out and now I can put more in and tighten it. The old tubing was hard and just broke at the connection. I'm betting the solenoid is ok, and will go back tomorrow(?) to put it back in. I also have more than enough 1/4" vinyl tubing to replace what's there, as well as some 1/4" Stainless Steel tubing and a SS tube union.
I really hate having to pull that (or any) fridge out from the wall to work on it. The kitchen doesn't seem that narrow with it in place, and the 1955 vintage floor tiles and the hardwood under them really don't like being disturbed (or wet).