To leave the converter on all the time during non camping use we need a float mode in the converter or charger.
13.25 VDC area is float with limited amperage to go with it
13.65 VDC area is normal charge voltage with high amperage pending the battery needs.
As you can see there is not a lot of difference when doing battery testing but a 2 decimal place digital volt meter can pick up the differences.
Try your meter when you know you are charging the battery, it should read in the 13.6 to 13.7 area on normal charge. Then you know the meter is working well enough to trust that when it drops down to 13.2 or 13.3 you are in float mode. If wanted you can do an amp check, need milliamp range and at least a 10 amp fused meter for opp's.
Some of the Centurion units did have float. Yours may have it and if so then leaving the unit plugged should not boil out the battery so fast. However, still check the electrolyte level every month or so when plugged in full time non stop. Once you can trust it, it is not boiling down the battery too fast, you can better predict.
I have one of the newer 3 stage plus desulfate mode converters I added and I use a battery Minder with desulfate mode. I top off the battery with distilled water in the spring and all year it will not drop very much. I am plugged in all the time (even in winter) except when towing and boondocking. It took the higher end converter and time monitoring it to trust it, but it now has repeated this for the 7 years and I'm still on the same batteries. I know I'm pushing the time when new batteries will come. I thought for sure this year when boondocking for 14 days they would flair up, but they didn't.
Good luck and hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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