Reverse lights stay on after ignition turned on. The fuel pump was recently replaced after it failed. I’ve replaced the reverse switch and tried a brand new ignition switch just to rule it out. I’ve removed bulbs until I can diagnose the issue. Is there a relay to check? If so, where is it?

What is your experience with auto electrics, or electrics of any sort?  Do you have a test meter and do you know how to use it?  Do you have the wiring diagram for the vehicle - if not, you can get it at Ack's FAQ.

There are few circuits simpler than the reverse light circuit - battery positive to ignition switch to fuse to reverse light switch to reverse lights to chassis ground - there are no relays involved.

How much have you spent on parts & incorrect diagnosis?  Use a test meter to check for voltage at the reverse switch connections, if there is voltage on both connections, disconnect the switch and check the harness side of the connector - if there is voltage on both wires, there is a short in the wiring - if not, the problem is your new switch.

Remove the switch from the transmission, connect it to the wiring and depress the ball with your thumb - can you turn the lights on and off?