To quote Charlie Brown, "Good grief".
OK, I took my 8080 apart and had a look.
The horizontal yellow metallic cap just above the power transformer is a 150mfd@150v. The vertical orange cardboard cap is something at 350V. Can't read it. Those should be replaced, but I don't have them on hand. I tested them in circuit and they're not currently leaking and they're holding a charge, so for the moment they're fine. I put it back together.
It's the one on the right. On left is my 2972. Only external visible difference is the extra voltage switch on the bottom-left of the control panel.
I went ahead and sacrificed the AMP connector and built a
universal adaptor.
The black clips are filament, green is K (cathode), and yellow is G1 (1st grid). I checked a good 10BP4 and got identical results as my 2972. Then I checked a NOS 5FP14 radar tube that I've never tested before because it's an octal base (2972 doesn't support it). It tested .98 mA and 15 seconds life which is normal for NOS, so I guess the test function works.
I grabbed a 7JP4 from the junk pile. Never tested it of course (funky huge socket). It came in an eBay purchase that was mishandled by UPS. The deflection plates in it are broken loose from where they belong and just rattling around in there. No real hope of fixing that. I got a 7JP4 pinout diagram from the web and clipped on the clips appropriately and checked it out. For about 3 minutes there was no emission, then a little, and after about 5 minutes I had a 0.1mA reading and no life test. Pretty dead. I went to step 2, cleaning. Took several minutes for the cleaning light to glow dim, then a minute or so to brighten up. 20 seconds at bright, per instructions. Went back to step 1 and had a 0.8mA emission and a pretty poor but passable life test of 1-2 seconds. At this point normally you'd say "good enough", but WTF, the crt is toast anyway. I went to restoring mode. On bringing up the filament voltage I got a couple of bright flashes on the restoring lamps, like yoda described on another post. I'd never seen that before with my 2972 but maybe just coincidence. Anyway after the flashes, a minute later the lights glowed very dim and then slowly rose to bright over 10-15 seconds (normal operation). I cut the current twice and let it cool. Now it tests 0.95 emission and about 5 seconds on the life test. It would probably be very passable if it still deflected correctly. As it is, only Scotty can fix it, someday..?
So, long story short, I think my 8080A is functional. I'd be happy to take readings here and there if you want.
First off, the restoring lamps are in parallel so even before you repleced the open one you should have gotten a meter reading. At some point before 85 mA's you would have blown the other bulb though. Both bulbs have to share the .85 mA load. It's possible both bulbs were open, maybe the good one wasn't screwed in all the way? Even if, once you put the replacement bulb in, you should have had a current reading eventually.
If your test and cleaning functions work, the power transformer is ok. You should test each meter for continuity. Might be hard to do that in-circuit or might not. I could check that for you on mine. I'm guessing your restoring-current meter might be open..? That would be a tragedy. Parts are hard to come by except when an entire restorer shows up on that ePay place. A toasted meter would suck. But that's my guess from here. I can do some more digging tomorrow (Labor day holiday!).