Julian Bunn wrote:
It suggests either that there is a dirty switch somewhere, which isn't
making properly unless the plinth is pushed,

Sounds reasonable. It might be a mechanical switch; sometimes the metal
leaf of the switch is bent, and sometimes the thing that pushes on the
switch is bent or missing. Or, it might be an optical switch; these are
usually a U-shaped piece of plastic with an LED in one side and a
phototransistor in the other; a tab or blade slides into the slot of the
U to interrupt the light. (The LED is often infrared, so it may be
working fine, even if it doesn't look like it's lit.) Another variation
is an LED and a phototransistor in the same flat package; the light
reflects off a shiny spot on something that moves over the package.

or that the plinth isn't engaging into its fully closed position.

Also possible. Are there any rubber belts in the drivetrain for the
plinth? If so, they may be stretched/floppy and not quite driving it
as far as they should.

If it's all gear teeth, it's possible that one side or the other has
slipped a tooth, which means the plinth isn't being driven as far as it
should be. The service manual may have directions on how the gear
teeth should be aligned at assembly; if you decide to change it on your
own, mark or take a photo of how it was before you start, so you can put
it back that way.

On the plinth, at the left hand side, are two buttons: "Power" and
"Open". With the unit closed, when the Power button is pushed, the
plinth slides out. Oddly, with the plinth out, pressing the Power
button doesn't make the plinth slide back in - should it?

I don't know. I have never owned or used a turntable where the playing
surface slid out like that, so I don't know what the usual sequence is.

Also, in this closed position, the plinth can be moved from side to
side somewhat: this doesn't seem right, as surely the plinth should
be rigidly fixed while a record in being played?

Depending on exactly what's moving, this might be OK. If the plinth
and tone arm / cartridge support move together, then this is just the
suspension of the turntable. If the plinth can move relative to the
tone arm, then that may require attention... but I'd suggest getting
the open/close/latch operation working first.

Does the schematic show a solenoid or motor that would be involved
with sliding the plinth and maybe latching it?

Matt Roberds