My experiences are with the more-powerful ST-70, but I think the amps are similar enough for them to apply.
I didn't bother trying to reform old electrolytic capacitors; I just replaced them all. Fortunately, Antique Electronics Supply has the can capacitors used by older amps as drop-in replacements. They are, though, $35 each. But even if you decide to replace the cans with separate capacitors, they must be rated for high voltages (at least 350V) and so are comparatively expensive (I saw them at about $10 each; if anyone can find some for much less, it's fine with me, as I still have an ST96 tuner to re-cap).
I was able to get an Eico owner's manual, which is the equivalent of a service manual, and then some. It conveniently lists all the components and their values in the amp.
I decided to use a dimbulb tester, per the Antique Radio (Phil's Old Radios) site. It's a very simple circuit. The only difficult part is overcoming the awe of working with voltage out of the wall socket.
The Antique Radio site tells you how to use the dimbulb test to test the power transformer, then the power supply and associated capacitors. It worked out well for me. However, the site implies that the easiest test to pass is the lowest wattage light bulb; I got a 15 W bulb and it lit up bright as you please. And, it indicated...basically no problem with the amp at all. With high power hi-fi amps, idling current is enough to light up a low-wattage bulb.
So, you need to start with a high enough wattage bulb, else you get a false positive. The "So you want repair audio gear, eh?" topic in the DIY forum has guidelines.
It is not a straightforward test; I don't think my amp, with all the tubes in, ever worked with a bulb going really dim. But I got sick of seeing the thing sitting there and plugged it in, anyway. It played music just fine, at least from a CD player.
A phono source was horrendous, making a vicious low-frequency wail; "hum" doesn't do it justice. That was solved by replacing the input RCA jacks. I just used Radio Shack ones. They may have had a big wad of plastic on them, but it was easy to remove. By drilling a couple holes, I could mount the new jacks. With the new jacks, now the phono section behaved itself.
The ST-70, anyway, has quirks, don't know about the ST40. The on-off switch doubles as one channel's treble control. So, you turn the amp on and rotate the knob just enough to click on, then wonder why one channel is not producing. Oops, give it a little treble. Eico did not label their channels left or right but 1 (left) and 2(right). Looking at the amp from the front, speaker connections for channel 1 are on the right vs. channel 2, so you have to cross speaker wires. The connections for speakers are strange, all to accomdate some fancy level and phasing switches, and a center channel speaker. I found that phasing was correct with the "reverse" setting. And the volume control has a strange taper; turn it up just a little and the amp roars. Initially I thought this amp could rattle walls, but turning it up further didn't result in much more volume. Maybe they used a linear taper?
But you love the thing for its quirks, just like a family member, significant other, or pet.
It's a very capable integrated amplifier (if not the most handsome specimen you'll ever see).
