If it works with the second speaker connection I would leave it.
There are two main ways this fault can occur, one is that the switches have been set back slightly, this happens when one or more of the switches has been bumped backwards - often this happens in transportation/shipping - if so then he swithc will not depress enough to operate the latch, you just take the bottom of the unit off and loosen the bolts holding the front and pull the switch bank back out, it only needs to be wrong by perhaps a couple of millitmetres to cause the problem.There are also some other bolts inside I think, which means lifting the top off, its a while since I was inside one.
The other fault is rather differant, the latching plate underneath has to slide around and over a small plastic guider pip. If this is broken off it means trying to fabricate something and superglueing it in place - by far the best option,but not easy - or trying to replace the errant switch, - this is pretty much impractical, being the age it is the flexible pcb that goes to the tuner presets adjusters will be very fragile, it develops track breaks which are too small to see, but are enough to stop the radio working - these tracks can be bypassed by soldering insulated wire across the connections.
Unfortunately that's the least of your problems, its a *** getting that front panel off, you risk damaging the various slider pots, and when you do get it apart you still have to find a way of removing the dodgy switch from the switch bank - by this time you would be seriously considering forgetting the project and using it as a donor to repair other units.
The work involved is such that unless you do this sort of thing regularly and have all the tools and access to parts - such as a pile of other broken units for spares, you would be well advised to leave it alone.
I guess it is possible the latch mechanism is gummed up with old hardened lubricant, and a mild cleaner spray would free it - its never that easy.