I thought most of those relays are sealed cases, not meant to be opened. Usually when they fail either the coil of the solenoid burns out and will read an open circuit or some part of the contact will break off. Over time one form of fatigue or another will eventually lead to failure.
One simple check of the relay is hearing for the click a few seconds after it powers up. Every one I have with a relay it is clearly audible if you are close to it. If you can get in a good position to see them when the amp powers up you should see the contacts shift sides when it clicks. That circuit is nearly always set up to give the amp circuits a few seconds to stabilize before engaging the relay. Also there is a little transistorized circuit that controls the relay. Basically after that initial delay if the DC level at the output of the amp circuit is below a certain level, I think normally 1.5-3 Vdc varies by manufacturer and model, the relay the relay clicks in. If the DC level is above the target on one channel the speakers won't connect at all, the relay will stay open. I had an auction Yamaha CR-800 I got that had 3 bad output transistors and the relay did not click until I replaced them and the other collateral damage done when they failed (just 2 fusible resistors here - credit designers). With the caramel crystals and brown coating when I cleaned the board I think someone spilled a cola into it when it was on and it ran all down the amp board. If you are getting output at the speakers that would indicate the solenoid is okay or if damaged it would be the side for the left channel. On the schematic that circuitry that includes Qe11-Qe15 looks to be the the relay control circuit.
Simple check in first paragraph. More complicated detailed relay check in next paragraph. On the KR-7400 they have the relay in the middle of the amp board. Looks like on the KR-7200 they have it on its own board labeled X13-1240-10 with some resistors and capacitors. On my 7400 they have the board pins that the wires from other boards attached to clearly labeled and used the old wire wrap technique. Test clips are often safer than probe tips since once slip connection wrong contact points can create a short in the wrong place and zap - flash, maybe burned tip, maybe fried something. Power back on and off. Had number of times bright flashes but did not blow things, a couple of bad experiences teaches you to be more careful. You might get away with probe tips on this one, especially if yours had the kind where there is only a small exposed cone on the tip. Regular longer tips be careful, lose grip on one slips the wrong way may not be pretty. Remember the power supply and amp circuits can deliver a good pop in this thing. Don't try to take resistance measurements or diode checks on energized circuits, just ac or dc voltage.
Going by the connection wire wrap pins indicated by the schematic for relay board, looks vertically mounted like the 7400 in tight quarters hopefully all pins not too hard to access. Looks like control coil power comes in on pins 11-14. Checking continuity with unit off the spec sheets for the modern units indicates coil on a 24DC model should be in the neighborhood of 650 ohms. Just a ballpark, actual values may be a bit different. With unit on and control circuit energizing it should read around 24 Vdc between those two pins, at least greater than 19 Vdc. Usually on this type relay the coil has a resistance or is open. If the resistance is many times what it should be coil on its way out. If open its dead. With power off check continuity between the pair of pins 5-2 and 18-1. Should be open with the power off. Since almost no amp has zero dc offset, with unit on put negative tip to case, I usually stick the tip in one of the holes in the lower side of the chassis away from anything electrical and let it rest there. With unit on should see same DC values at those pairs of pins, one voltage 5-2 and other channel 18-1. Should see same voltage at speaker terminals. If all that checks should be okay. If pin 1 or 2 is lower than its paired pin there may be a problem with contacts.
The KR-7400 used an Omron MY4-02-US-24DC relay fortunately Omron is still around I think the current version of the relay is the MY4-02-DC24. My local Grainger indicates they have one in stock at the local branch for cheaper than Mouser wants, about $10. Relays like this are not hard to check. If your relay clicks a few seconds of being powered up the coil should be okay. If you just sprayed the contacts with some kind of contact cleaner, like CRC's QD contact cleaner I would think the contacts are okay. If in doubt you can trigger the relay manually. If you have a DC power supply, a lot of 18V cordless drill chargers probably use a 24 Vdc adapter or something close. The spec sheet says 80% rated voltage should trigger, so something that puts out above 19.2 Vdc should trigger it. Some small wire, such as bell wire you can buy by the foot at Lowes or Home Depot (some of that has been used in past repairs) and electrical tape you can tie into pins 11 and 14 to power the relay. Check continuity between the paired pins manually triggering the relay.