The ballast should have specs stamped into the metal. If nothing better, simply try taking the ballast to a good electrical place to do a cross reference of the parts.
You may need to go a higher level than the local big box to get the right folks to know what those numbers mean, however!
But then. is it possible that now would be a good time to move to LED to gain those advantages, even if slightly more expense now? There are times when we can change out the ballast and tubes to switch to LED and get some real improvements in overall function.
Less power used, less heat generated and longer lasting can be a real winner, especially in RV where battery usage can be a big thing to consider! There are times when LED tubes can slip right into the fixtures we have, without even pulling them down?