Bargman like this?

I installed those on our 2003 Escapade on Ford E450. I wanted something that used hard connections to the coach wiring, not plugs, adapters, etc. But I was disappointed that I had to marry the individual lights together before connecting to the coach wiring. In other words, I expected Bargman to have already connected the segments so I had only one Stop/Turn, one Running, One Backup, and One Ground per assembly.
Our lights flashed too fast too. I'd wanted to add clearance/turn signal lights to the sideview mirrors. Was planning to buy $40 LED "Lollipop" lights

but I was afraid I'd still need resistors, so I got $10 incandescent ones and the flashing came out right.
But back to your situation. My best guess is that you could have mis-connected the segments of the new lights and created a short or ground path.
Or, does the chassis use the Powertrain Control Module (PCM) to flash the signals? Just thinking if a computer module is involved, he situation could be a little more complicated.
But, then, it WORKS. If it works day and night, brake on or off, then maybe time to set curiosity aside.