Let me start with: I do not know if I will ever forgive them for dropping the A7. Yes, I do realize that the EPA was coming, but they had the best performing 350 out there, bar none. The Yamaha RD-350 always won the overall rating by Cycle World, but the A7 was always the top one in performance.
When you get to meet with BigSpecBear, take a voltmeter with you. That will tell you quite a lot. When the DryFit battery is fully charged and taken off the charger, you may measure an open circuit voltage of about 7.0 VDC. One that has been sitting for a few hours will probably drop down to about 6.3 VDC and sit there for a long time. You can also check the battery voltage when it will not charge the 60 CT-4 any longer. Normally I do not want to see mine at less than about 5 VDC. At that point, they really do need to be recharged. If after a normal full charging, it does not rise to the standard full charge voltage of about 6.9 to 7.0 VDC, or it just does not seem to last very long when it has been recharged, it may be time for a replacement DryFit.
The DryFit battery type may also be called an AGM (Absorbed Glass Mat), SLA (Sealed Lead Acid), VRLA (Valve Regulated Lead Acid), or some other similar non-spillable or non-liquid electrolyte lead-acid battery. It will not have any vents or caps on top to check the electrolyte level. Do not try to use a motorcycle battery in this application; you know what can happen if you lay the bike down and it is there on its side for a long time, and later you see what has happened in and around the battery box. And, in addition to that vertical ridge on the side of the case, the DryFit battery contacts are very different from the normal motorcycle battery posts with the lead plated brass nuts, washers, and bolts, or the special attached wiring and terminals.
You can get a perfectly serviceable Digital VoltMeter (DVM) at Harbor Freight for about $10.00. It also has lots of applications with the electrical system on the bike.