[Boots]

I would say there are a number of things you need to check...

The delay in operation when cold would suggest to me that a fluid and filter change would be a good idea.

If the select button is sound, as you suggest, the relay may be at fault but 'in the 4th gear switch' on the main gearbox also needs to be checked.

My 740 will show green 5 and both the relay and the solenoid on the OD will click in and out with just the ignition on (i.e. motor not running) so long as the stick is in the 4th gear position.

You need to methodically work through the suspects testing each one, starting with the electricals.

One way to check if the 4th gear switch on the main box is duff is to have the ignition on, keep the OD button pressed and then move the stick into 4th and waggle it around some. If the green light/OD solenoid flicker in and out as you waggle, the 4th gear switch will need replacing.

If you can't get any green light/OD solenoid activity at all then the relay or wiring/fuse/earthing is likely the problem. Poor contact where the relays plug into the fusebox is a common problem on older cars and it is self exacerbating. A poor contact presents high resistance to the circuit causing excessive heating of the contact. This heating increases the resistance due to tarnishing/distortion and so on until eventually the contact burns out. It would be worth checking the seating and condition of the contacts on the OD relay in the fusebox.

This circuit should be reasonably easy to diagnose logically with a multimeter or test lamp...