Been a while since I had an 85 but IIRC you can replace that core
without pulling the instrument panel. Seems like you remove the screws
for the cover from inside the passenger foot well, watch out for the two
on top that can be hidden and one that is a stud going into the engine
compartment. Clamp and remove the hoses under the hood. Remove the
straps and the core. Reverse this to install the new one.
There is a tutorial here with pictures
I've done an 84 & a 94 S-10 Blazer. It helps to have a 1/4" socket set
with extra and/or long extension bars. For me, the bolts that hold the
2 straps on the core itself were hardest to deal with. Don't remove
the 2 uppers, just loosen them. I did not remove the ECM, but did
remove radio and glovebox. Just loosen the dash itself.
3/4" and 5/8" Easiest method would be to buy one of the coolant flush
kits that includes T fittings that will fit all the different sizes.
Plus when your done it provides an easy way to flush the system. Like
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