[fauXGT]

I am currently messing with a Speedway 22 circuit harness before installing, and it does have a separate spot for a flasher module for hazards only.
Did hazards work before the LED install.
A modern column will mostly use 2 flasher modules. One for turn, one for hazard. But I'm installing the factory AD column and an old school 7 wire Napa turn signal assembly from the early 60's. It has a built in hazard activation thru the turn signal flasher, so I'm not using the hazard plug on the panel.
Check to see if your fuse panel has 2 spots for flasher mods. If you have a modern column, the hazard circuit may not be wired in from the column to the panel even though you plug in a module.

Edit. The harness you are using is identical to mine. kitty corner from the turn mod plug is the hazard plug. A modern column with the hazard button on the side I'm pretty sure requires the wiring of the separate hazard circuit. The pushing in of the hazard switch on the column re-directs the signal to use the hazard on the panel. I set up LED's on a 91 GM with using the identical flashers, and the only issue was the alternating flashing on the front side lights when park lights were on. IT switches the polarity on an incandecent bulb which won't work on a LED. Fixed with wiring thru a 3 to 2 trailer mod. Much brighter lights, but a PITA to set up.