I'm not familiar with the 124 Spider, but am very familiar with the 124 Sport Coupe, however I believe these 2 models are nearly identical, mechanically and electrically, so....
The red wire from the ignition switch to the starter solenoid should only be live (i.e. 'hot') when the key is turned to the start position.
Are you sure this red wire is connected to the correct terminal on the rear of the ignition switch? Iirc, it should go to the terminal marked '50'.
Also, iirc the bunch of cables that connect to the rear of the ignition switch are covered by a plastic boot/cover. When pulling back this boot/cover, it's important that the loom/bunch of cables is held and the boot/cover is eased back. I've seen it happen that some of the cables can be slightly pulled (i.e. not completely disconnected) from their terminals on the rear of the ignition switch, enough that one of more cables can make contact with another cable, thereby becoming 'hot' at the wrong time. It's worth checking that each cable terminal is tight on it's connection, I've sometimes had to tighten the terminals by squeezing gently with a pair of pliers, to ensure a good connection.
If all the cables are correctly connected at the rear of the ignition switch and no cables are touching, then if terminal '50' is live without the key being turned to the 'start' position, then surely the ignition switch is faulty (perhaps shorted internally)? (despite your tests - you didn't say how you tested the ignition switch, starter motor and solenoid). I've seen one or 2 ignition switches which had melted internally, but this usually resulted in failure to make a contact at the appropriate key position.
In general, for the starter motor to work, you need a power feed from a (well-charged) battery to the starter motor main terminal, the starter motor/engine to be earthed/grounded back to the battery, and power to be applied to the small blade terminal on the starter solenoid.
Maybe try disconnecting the thin red wire from the solenoid and connect a separate jumper cable from the solenoid blade terminal directly to the battery positive terminal? If the starter motor now spins-over the engine, at least you'll now know that the starter motor, solenoid, battery, battery cables and grounds are ok. The problem then is most likely to be the ignition switch or that red cable.
Hth,
Al.