Condensate Drain Question

Hi,

I have 2 Carrier AC units. From what I’m seeing in my attic, the primary condensate drain line for both units join together into one and go down into the wall that is behind a bathroom sink.

A few weeks ago I had a clog in the line that primary condensate drain line is connected to. I expected the condensation to start draining out of the secondary drain lines (which are just 2 PVC pipes coming out of the soffit near a window), but water started coming up the sink drain and filling the sink basin. The float switch never tripped because water wasn’t filling up the pan. This seems like it could’ve flooded my bathroom if no one had been home to notice the basin filling up.

Any idea how to prevent the basin from filling up so the float switch and secondary drain can actually do their jobs?

Thanks!