Backup Alarm misbehaving

Hello
My 03 EB 4WD 5.4 has the 2 backup sensors mounted in the rear bumper.
MOST of the time, when I put it into Reverse, I get an error status on the dash along with a single 1 second tone that says CHECK BACKUP or something similar.
Once in a while, maybe 1 out of 10, the backup system works great, giving the expected warnings as I am getting close to something as I back up.
Since it is intermittent and offers no error codes on the OBD2 system, I am clueless as to where to start looking for the cause and cure of this situation.
The dealer basically said that when/if it fails 100% of the time, they can look at it and try to find the problem but looking for an intermittent would be potentially very costly.
I appreciate their honestly in this regard.
Any help would be appreciated.
Thanks

FYI you hasve 3 sensors in the rear bumper the two you can see and there is a radar sensor about mid point behind the bumper check under the bumper and you should see the wiring for it

Thanks for that info.
I was not aware of this at all.
It seems odd that when I get the "Check Backup Aid" notice on the dash, that there is no error code coming up on the OBD2 port.

I had a similar problem except mine stopped working and the check Backup Aid always came on when put into reverse. I had a dealer run a body module code check and it had a code of C1983 which was the rear radar sensor. The OBDII reader is not a body code reader.

I had the same issue "Backup Aid always came on when put into reverse" on my 2017 Expedition. Everywhere I searched the recommendation was one of the sensors were bad. I changed each of the 4 sensors with no luck. I located the backup sensor module behind the second row seats on the left side behind and below the seat belt panel. I replaced the module as well, not the issue. I took it into the dealer and they stated the sensor on the right side was bad and wanted $500 dollars to remove the bumper cover, paint and replace the sensor. The sensors can be changed without removing the bumper cover. I decided to check the wiring and bingo 1 of the 3 wires were broken. I ordered the backup wiring harness for around $40 and replaced it. Problem solved.

I'm interested in the fix for this too. Mine used to work, then it started working intermittently, and now it hasn't worked in probably 6 years. Always get the "check backup aid" when I put it in reverse.