Backup 2 distinct HDs to their own backup drives

I hope I can explain this clearly.....

I have a mid-2017 27" iMac w/40GB ram running Catalina and need recommendations for backup software. I have a 1TB backup drive for my 500GB internal HD and a separate 500GB to backup the 500GB external drive that is solely used for Lightroom files. All my images files reside on the LIGHTROOM drive and NOT on the internal HD.

I want the 1TB external to only backup the iMacs internal drive and the other to backup ONLY the Lightroom external drive. Right now, Time Machine does a complete backup of BOTH drives onto EACH backup drive anytime it runs.

From what I've been able to find out so far is that Time Machine can't do what I want. To workaround this limitation, I have to configure Time Machine to only backup one drive at a time by "excluding" one drive which means going into Time Machine preferences EVERY TIME I want to perform a backup to one drive or the other. Has anyone run across this situation and found a backup software solution that works? In case it matters, I'm not interested cloud storage.