turn signal and brake with sequential

I have a 1990 Firebird.  At the taillights, I have signal wires for each turn signal (left and right) and brake signal wires.  The way it was setup, the outer lights would blink as the inner 2 lights were the brakes.  However, putting in a STS-1 module from webelectric brings up some issues.  I'm able to get the lights to sequence, but now I don't have anywhere to hook up the brake signals to.  The module is referring to cars having brake/turn signals in 1 wire.  Well, as stated, I do not.  If I hook up the brake signal and turn into 1 connection on the module, when the turn signal is on, and I hit the brakes, the turn signal stops and the blinker is "frozen" until I let off the brakes.

So, I think what I need to do (without having to run more signal wires from the flasher to the back of the car), is have a momentary relay in place.  What it would do is, when the turn signal is blinking, it will remove the brake signal from the assembly, so that the module can sequence the lights.  The only problem is, the turn signal is "pulsing" a 12V signal, so the relay will be clicking the brake signal on and off.  That will not work and/or mess up the module.  So, from a pulsing input, I need the coil on the relay to stay constant until the pulsing stops, and then reapply the brake signal so that my brake lights work.

I hope this makes sense and is an easy solution!  Thanks!

I need a relay that when given a pulsed 12V (in about 1 second intervals), will provide a constant output (keeping the coil energized without clicking it on and off with the pulses).  But when the pulsing stops, I need the coil to de-energize right away also (not staying on for 5 seconds after, etc.).

Is this the setup:

https://www.the12volt.com/12voltimages/constantmoment.gif

Or it may be this one:

https://www.the12volt.com/relays/page5.asp#pts

10kuF seems pretty excessive. And the description says to increase the cap for a longer output. If this diagram describes a "constant" output, what would be a "longer" output?

Thanks!