Regarding ESR testing, the actual test is accomplished by applying a low amplitude AC signal across the capacitor under test and measuring amplitude across the capacitor. Expensive ESR testers use a sinewave signal, but squarewave will also work. Here is a link to a DIY test adaptor for checking ESR with a scope or a DMM with an AC 200mV or 300mV range available.
http://octopus.freeyellow.com/99.html. The circuit is simple and powered by an ordinary 9V battery. The author begins with a simplified version based on a hex inverter I.C. and does an excellent job of explaining the operating principle and the limitations of the simplified version before going on to provide a schematic, parts list, description, and operating instructions for the improved final version. By using a dual trace scope and applying the direct output to the other input, direct comparison of the two waveforms on the scope screen is possible. Paper capacitors should be replaced ASAP when restoring a vintage set to working order, but electrolytics with sufficiently low ESR, low leakage, and capacitance within factory-specified tolerance may be left in place once properly tested and re-formed and will thus minimize the need for re-engineering and the potential danger of replacing a superior part which has survived 50 or more years with a modern part whose reliability may be questionable due to cheap construction.
I will be constructing one of these for evaluation and will post my findings here.
Doesn't the fact that the vast majority of these sets that have been spared from ending up in landfills can be brought back to life once they find their way into the hands of those such as ourselves who care enough about preserving them to make the effort factor into the reason why we love them so much? Restoration would not be possible at all had the vast majority of these sets not been so well-enginnered and well-constructed in the first place.
"Time Capsules" were one of those 70s phenomena that I seem to remember, where items from the era were stored away to be reopened decades later. I challenge someone with the means to do so to arrange for a suitable restored and known-working vintage set, metered Variac, sealed bag of new "Orange Drop" caps, restored B&K TV Analyst, modern cheapie TV, DVD player, test pattern DVD, service literature and instructions to be sealed away to be reopened in perhaps 50 years just to see which set still works.