Hey Al - wecome! I'm new here, too. Very cool place, huh?
Those appear to be the ST-EF50 series which has covered the Altus and Acera groups for a few years now. Yours being 8 spd, I am betting Acera ST-EF50 (or 51 or 52 or it looks like 29L in the #3 pic) is molded into the unit on the underside near the mounting clamp.
You mention 'ears' and this confuses me. I read it 3X to be sure I didn't miss something, but that is no guarantee! There are no 'ears', per-say. This cover is attached by the two, small, phillips-head screws to the L & R of the indicator button in your first pic.
Take a look at your 2nd pic... the shifters don't match. One or the other has been replaced. Still focused on the 2nd pic... see all of the scuff marks on the housing? I can assure you - that is not 'trail rash'. In the passed 20 years, I have come to recognize that as 'garage rash'. Bike has been upside-down on cement while being worked on. And slid. OUCH!
The small scrapes on the top of the stem face-plate reinforce my wild guess.
With all of that said - your problem can be solved by any LBS that has an account with QBP or Shimano. New upper housing should be $10 USA, max. $6 for real. Do not do Ebay with the question that you asked. PULEEEZE! That only upsets a mechanic. For less than $50, you can buy a Brand New, Improved, GPS Enabled (kidding) pair of 8 spd ST-M410 Alivio ST (ST = Set, integrated, as opposed to SL = Shift Lever and BL = Brake Lever). As an added bonus, if you act NOW, we will include the inner cables at no additional cost! You heard me correctly! At NO ADDITIONAL COST!
I just had to do that to lighten your frustration. Been there. Was bummed. Feel better now. Ahhh.
Wheelies don't pop themselves. (from a QBP fortune cookie)
By ears I mean there is still part of the cover under the screws A(The covers are now in 3 pieces instead of 1). I have a bike stand so it hasn't been upside down since Ive owned it except the other day when I panicked and hit the brakes to hard. Those V-Brakes will invert you in a hurry if you are not used to them. The 1st thing I checked was the covers. My Trek has a different style so maybe another set of them for this bike. They say Alivio right on them. It has XT Derailleurs so it seems both bikes have lower grade shifters then Derailleur. I few years back I had piles of this stuff but gave it all to the Bike Library thinking my riding days were over.
I think RoBar has hit this right on the head, sort of speak. Personally I would go with new shifters and upgrade if you are going to do much riding on this bike.
Have a great day
lol nice replacement
Good maintenance to your Bike, can make it like the wheels are, true and smooth!