This isn't by chance a York unit? - We've had 3 units in the last 3 weeks with the same issue. The relay on the board that controls the indoor blower is bad and the board would need to be replaced..
Unfortunately, the blower won't work in heating mode the way you have it wired right now. The board controls blower operation in heating mode without energizing the compressor contactor.
The Carrier boards are available either directly from your Carrier rep, or you can try searching by board part number to see if there is a generic replacement. The part number should start with 2 letters Usuallk HK###### XXXXX They are almost all made by ICM controls
I haven't found an aftermarket source for York boards yet - Carrier equivalents are everywhere online and in the general supply houses for almost all of their HH and HK boards. I currently have 2 rooftop units running with the blower motor powered by the compressor contactor to bypass the blower board. Their on my list to repair before colder weather hits
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it still shows as an open question - you just click on "accept" and it closes out