The "S" terminal on the solenoid should have the Red w/Light Blue stripe wire, it almost looks like you have the Red w/Lt Green stripe on it. Can't tell from the pics, the color is a bit off.
I am in (as usual) total agreement with HemiKiller, making sure the correct wires are connecting to the Starter Relay's smaller terminals. And even though your photo does not show the "S" and "I" terminal wiring color very clearly, it does show the color of the insulating hood coverings. One is a "blue-ish" looking color, and the other is a "green-ish" looking color. I have found the insulating hood covering colors are correlated to the wire stripe coloring, as shown a little more clearly of this attached photo from a colleague who sent this to me the other week.
Going by the color of the insulating hoods it seems you do have your two Starter Relay smaller wires connected to the correct terminals. It is best to go by the wire coloration, as I have only observed the difference of the terminal insulating hoods when I took note of it, and until recently never bothered to see if there is an intentional difference in there colors or not.
If the Red-Blue Stripe wire (Circuit #32[a]) is correctly connected to the Starter Relay's "S" Terminal, where the wire leads to the Neutral Safety Switch, it will only have power when the Ignition Switch/Key is in the Start/Crank position. Any other time it should have no voltage.
As for the Reg- Starter Relay's Red-Green Stripe wire (Circuit #16), it should be connected to the "I" Terminal. When cranking the engine over that terminal/wire should show cranking battery voltage, which will usually be between 9.6 and 10.5 volts. If you have less than 9.6 volts while cranking you have a battery that needs charging and/or you have one or more connections in the vehicle's wiring that has excess resistance - usually it is a low or failing battery.
When the Ignition Switch/Key is in the Run position the "I" terminal/wire fir Circuit #32 should have aa reduced voltage coming from the resistance wire circuit from the Ignition switch. That reduced voltage should be between 4.5 and 6.9 volts, s it is connected to the Ignition Coil's Positive Primary Terminal (still a Red Green Stripe Wire).
I have attached a relevant section of shop manual snippets for you to refer to. I also have the relevant circuit schematic on my Google Drive (too large to attach to this post). The link to download that schematic is:
If you are getting full battery voltage at the Starter Relay's Circuit 16 wire in the Run position (about 12 - 13 or so volts in the Run position) it is an indication that the wiring has been altered to provide non-resistance voltage reduced current to the Ignition Coil. This is sometimes done when folks replace an oem Ignition Coil with an aftermarket Ignition Coil in the expectation of getting a "hotter" spark at the spark plugs. It is also sometimes done when someone has installed an electronic ignition system along with a new 12 volt Ignition Coil. Please be aware, the oem Ignition Coils are designed to operate at 6 volts, not 12. They will work with 12 volts, but may overheat. Further, a "hotter" spark does not occur just because a higher output Ignition Coil is installed. An Ignition Coil only puts out as much is needed to complete a circuit, to include jumping a spark plug gap. The spark may remain active for longer (a natter of microseconds) when more potetial voltage is coming from an Ignition Coil, but from a practical perspective they won't do much unless you make other changes to the ignition system (widen the spark plug gap, for instance).
The reason I bring up the prior paragraph is because I have seen modified ignition systems where folks will use a relay to provided full battery voltage to an ignition system's primary circuit, and the triggering voltage of the relay may come from a switch voltage source, but said triggering circuit may be provided with voltage that does not necessarily end when the Ignition key is turned off. It can get complicated pretty quickly.
If it looks like your primary ignition system has been altered, you will need to trace down all the related wires, and relay if one is present, and alter the wiring to make certain the trigger voltage to the relay is coming from a circuit that does not fdeed back into a circuit that might be left on when the Ignition Key is put into the Off position. Like I said, it can get complicated in a hurry as there are so many ways an ignition system can have its wiring altered - and not all of then are good, although some of them are done in a correct manner. (using the Stator terminal Circuit #4 (White with Black Stripe wire) from the alternator is a good way to trigger a relay to engage a relay despite being AC current and 1/2 battery/alternator output voltage, as when power is cut to the alternator field circuit, the Stator terminal loses all power - absolutely.
I hope you post the solution to this situation once you find the cause. I am really curious what is afoot.
