Do I have to keep an AGM battery on float charge 24x7?
The short answer is: No, you don't have to keep a charger connected constantly to keep your battery healthy.

The longer answer is: A naiive timer on the charger may or may not work, depending on a lot of factors.  AGM batteries can have a self-discharge of as low as 10% per year (which is quite good).  For such cells, a full charge every few months should be adequate to keep your battery charged when you need it.  The catch is that you want to make sure that your battery is really fully charged each timer cycle.  If the timer turned the charger off prematurely, the battery state of charge could get lower and lower each cycle, leaving you without power when you need it.

For a simple solution (and assuming your charger is appropriately sized), try turning your charger on for several days every 2 or 3 months.  This should ensure that the battery is fully charged each cycle, while still allowing you to leave the charger disconnected the majority of the time.

For an EE-centric solution, look for a lead acid battery charge management IC that can give you a reliable indication of the transition from bulk (constant current) to polish (constant voltage) charging, and ideally provide a timer for the duration of constant voltage charging to indicate when the battery can be considered fully charged.