The hot water trick works if the tar is still somewhat pliable. After 40+ years though, most of the tar in the stainless tanks around is pretty dried out.
The Innes formula for the black goop/tar is equal parts Gilsonite bitumen (check the bay), thickened linseed oil, and heat. Thickened linseed oil isn't "boiled linseed oil". It's raw linseed/flaxseed oil that has been cooked down by about 25%. A VERY smoky, messy, stinky project to thicken linseed oil, and only do it OUTDOORS, in a disposable pot.
If you are a resto-nut and need to have the tank restored "as built", use a heat gun, a thin putty knife, and a truckload of patience to melt out the glass and slate. Don't pry, just methodically blast the frame until the tar lets the glass go. Then clean out the frame and glass with the heat gun, carburetor cleaner, and a bristle brush. This will take at least a day and you'll break at least two panes doing it, no matter how careful you are.
To use the newly mixed up tar, roll it out thin (1/4") between waxed paper sheets, and cut strips to line one pane area at a time of the frame. Blast the frame with the heat gun until the tar is very gooey, and quickly set/press the pane/slate in place. Repeat, x4 more times. Once the tar cools, trim the oozed tar from on the outside areas with a razor blade. If you did everything right, there's a pretty good chance the tank will be sealed. The bigger the tank, the harder it is to keep all the tar hot during glass setting.
FAR easier is to clean out the frame (as above), carefully measure and then chuck the old 40+ year old scratched up glass pieces, get brand new glass cut for all the panes -and- a thick piece of plate glass for the bottom, then use black silicone to seal them in place. THICK beads in the frame, and then seal all the seams, too. Save the slate bottom, sand the edges and corners round, lay a layer of thin (1/8") packing foam sheet in the bottom of the tank, and just lay the slate in on top of it. The bottom glass is now protected from any point pressure from big rocks, etc.
You can try the quick-fix by smearing a bead of silicone on all the seams of the tank, as is, an you'll probably get it to seal for a couple years. Silicone, in my experience, starts to peel off the slate after a while, though. "A while" may be a few months to a few years, depending on how clean the slate surface was before being sealed with silicone. The original sealer goop was petroleum based, and any contamination of the slate surface by it will cause silicone adhesion issues in those areas. Lightly sanding the slate where you will be adding silicone, then rinsing, drying completely, helps. Just be careful of the glass when you sand.
I've restored several dozen stainless framed tanks now, here are a few pages of tank disassembly: