The charger should be designed for this lead flees battery and have protection against overcharging. The voltage are decreased when the battery are fully charged.
Do you think it was reasonable to put in a timer so that the charger only runs eg. an hour a day?
Here is how I would find out:
First connect the charger to the battery with no other load connected. Use your DMM to monitor the battery terminal voltage for the first few hours. If the charger is a modern u-processor controlled charger, the battery voltage will slowly increase up to ~14.6V during the first few hours (how long depends on how much the battery was discharged initially), and then the voltage will drop to ~13.2V and remain there until the charger is turned off (or disconnected from the battery). A momentary interruption of input power, or disconnection from the battery, will restart the cycle over again.
Now try it with the load connected across the battery. One possibility is that the charger tries to get the battery voltage up to 14.6V, but due to the load current, it cannot, and it keeps trying forever. If that happens, you will damage the battery if the final resting voltage (after several hours) is higher than 13.8V. This would be because the charger is not designed to drive a load in parallel with the battery.
Another possibility is that the charger switches to the lower voltage, and now the load current causes the battery voltage to sag below 12.9V, which over time will chronically undercharge the battery, causing it to sulphate, ruining it.
If, after several hours with the load connected to the battery, the battery voltage rests at >12.9V but <13.6V, then you are ok to leave the charger connected all the time.
The timer idea should be used only as a last resort, if the charging cycle hangs up.