Adding a voltmeter is a good idea. Learning what it means is also important.
There are three basic voltage profiles. They are charging, discharging, and static. Static means neither charging nor discharging for a while. For accurate static reading wait 4 hours after charging has stopped. Watching the voltmeter will teach you how long it takes before voltage stabilizes.
Charging voltage profile is a combination of charger (either converter or solar) and the batteries used. It starts at the existing voltage and slowly rises. High capacity chargers raise the voltage faster. Smaller batteries raise faster.
Voltage usually raises to more than 13.0 volts. I had an older one that rose to 13.3 volts and stayed there. The one I have now is more complected. It raises to 14.4 volts for 4 hours then drops to 13.6 volts. After a few days of stable current, it drops to 13.2 volts.
13.2 volts is great for long term storage for all lead acid batteries including AGM batteries. 13.6 is OK long term for flooded cell batteries. 14.4 volts for longer periods will damage AGM batteries and will cause flooded cell batteries to consume lots of water. 15.0 volts is sometimes used on flooded cell batteries to "condition", "equalize", or recover from storing at low voltages. Don't do this for long periods. Don't do this on most AGM's. Always check and refill water levels after high voltage charging.
I wish you good luck and happy trails ahead!
Choosing An RV Battery https://www.irv2.com/forums/download...do=file&id=231
Battery University https://batteryuniversity.com/
How does the Lead Acid Battery Work? https://batteryuniversity.com/learn/...ased_batteries
Charging lead acid batteries https://batteryuniversity.com/learn/...d_acid_battery
How to Charge and When to Charge? https://batteryuniversity.com/learn/...o_charge_table
How to Store Batteries https://batteryuniversity.com/learn/...tore_batteries
Summary of Do’s and Don’ts https://batteryuniversity.com/learn/..._battery_table
Charging with Solar, Turbine https://batteryuniversity.com/learn/...ar_and_turbine