The lack of response might be because of some confusion concerning how the mirror lights were integrated into the factory turn signal circuit - particularly the sentence in italics:
I ran my wires for the turn signals within 6 inches of the turn signal bulbs in the fender.I however now realize that when the running lights are on The polarities are switched on the wires.
But whatever: To answer your question – yes it can be easily done, but it will require a 5-pin relay. Just a common off-the -shelf Bosch type will be fine.
In addition to the NO terminal found on a 4-pin relay, a 5-pin relay also has an additional terminal that is connected to a contact that is normally closed (NC). The terminal designations are standard across all makes of relays – (87 is NO and 87a is NC)
Here go to this site and read this:
http://www.bcae1.com/relays.htm
It is a good, concise description of how a standard 5-pin relay works. When you're finished, you'll know as much about 5-pin relays as anyone.
Then go here and read - I think this is pretty much exactly what you want to do:
https://store.ijdmtoy.com/5-Pin-12V-40A-SPDT-Relay-Socket-Wire-p/aa1126.htm
In your case - if I understand the scope of the modification correctly - you want to isolate the mirror directional lamps from the rest of the T/S, P/L circuits.
Yet you still want them controlled and supplied with power by the factory flasher. Also, when the T/S's are off (and the H/L switch is in either the P/L or H/L position), they will be steadily illuminated. Basically they will operate just like the rest of the turn signals.
But I'm not quite sure what this means - so I could be all wrong:
Is there any way I can wire a relay or something like that to take either a positive or negative input and have a singular output.
Just quickly - cause I am f'in beat tonight - here is what is involved. See the image of a 5-pin relay at the bottom of the page:
1. To provide a pulsed signal to operate the relay coil (and make the mirror lamps flash I time with all the rest), you'll need to tap into the pulsed factory T/S circuit someplace. I won't try to tell you where to make the actual splice - but I strongly suggest you cut into the PPL 16 lead that runs the between the load side of the flasher up to the directionals switch in the column.
2. When you have completed that splice, run your lead up to the coil positive (terminal 86) and ground the negative side (85). That is it for the control side of the relay. Don't worry about disrupting the rest of the circuit, the load required to operate the relay coil is minimal and should have no effect.
3. Now for the current carrying portion of the relay (i.e. power to the contacts that will actually supply the mirror lighting). First, run a lead from terminal 3 on the H/L switch (3 will be jumped to an adjacent terminal which that supplies parking, marker & plate lighting). The harness connector for terminal 3 will be an empty cavity - unless you have roof markers or a factory digital clock in your radio.
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Connect the other end of that lead to terminal 30 on the relay.
4. On the load side of the contacts (term 87a), run two leads - one to each mirror.
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With the relay wired this way, when you turn on your parking or headlights, the mirror lamps will illuminate (steady) as well. But, when you operate the directionals, the power to the relay coil (from the flasher circuit) will also start cycling on/off. Which will cause the NC relay contact to open/close. The mirrors will blink in time with the rest of the lamps in the circuit.
One thing to be aware of, by wiring it this way, the mirror lights will be 180 degrees out of synch with the directionals. But that will look good - just like the marker lights.
