Need a bracket to fix a parking sign on square parking lamp post

I would use these:
https://www.grimco.com/Catalog/Product/AB-10

works fine on both square and round posts

 

I would not trust those clamps on square posts.
We had a similar strap fail on a 6" square pole - holding up 6ft banners. Looking back it was stupid of us to install using the straps. With the screw slots in the band, there is not much material to cover the stress points going around the corners. Could have just been cheap bands but we ended up making our own.

 

If they are under 18x24, you could use VHB with an ACM sign panel. Obviously wouldn't work if they are perpendicular and not flat against the pole. We did 12 like that, at request by the customer, and you can practically hang from them. Been through tornadoes and everything. We're pretty surprised at the results.

 

I suspect a local welding shop could make up a couple custom brackets for about $75.00.