My Agility is a 2009 model and I am only aware of two fuses inside the battery box. I also do not know whether the wiring on Agility's has been changes since 2009. Some time ago I saw a comment which indicated that some models might have an engine kill Switch. My Agility doesn't have a kill switch - the ignition switch is the only switch which can kill the engine.
To eliminate the possibility of another fuse somewhere, I would use a multi meter to do a voltage test at the ignition Switch. Your scooter should only have two wires connected to the ignition switch:
1. one incoming Positive feed (+) wire from the battery (via a fuse). (Will always have (+) power when the fuse, wires, and connection are good - even when the ignition switch is in "Off"
position).
2. one outgoing Positive feed (+) wire . (Will only have (+) power when the key is in "On" position).
I would ground the multi meter directly to the BATTERY, and see whether I get a voltage reading at ONE of the two terminals at the ignition switch.
If you do get a Voltage reading, (even when the switch is in "Off" position) it means you found the incoming wire from the battery and you don't have to worry about another fuse.
If you don't get a Voltage reading, it means the scooter might have another fuse - or you might have a poor (fuse ?) connection, or broken wire between the battery and ignition switch.
If you got a Voltage reading, you can turn the ignition switch to the "On" position, and do a similar Voltage test on the 2nd terminal.
(Again, ground the multi meter to the (-) on the BATTERY).
If you got a Voltage reading again, it means the ignition switch is not faulty.
If you didn't get a reading, it obviously means the ignition switch is faulty.
If you found Voltage on the 2nd terminal you can then repeat the 1st Voltage test again - but this time ground the multi meter somewhere to the scooter's CHASSIS , not the battery.
If you don't get a voltage reading, it means you're having a bad earth connection somewhere.
Just some ideas to start eliminating some possible causes of the problem...
P.S.
Just some observations on my Agility when the ignition swith get switched "On". You could compare this with your scooter:
1. Dash lights and horn are dead - it only works when the engine start running. (In your case it will not come on, because the engine doesn't start).
2. Brake lights are dead - it only comes on when one of the brake levers get pulled, with ignition switch "On". (You can try this on your scooter - the brake lights should work when you pull one
of the brake levers + ignition switch "On").
3. Rear lights are dead - it only works when the engine start running. (In your case it will not come on, because the engine doesn't start).
4. Indicator lights works with ignition switch "On" - the engine doesn't need to run.
5 Head lights should come on with ignition switch "On". If I remember correctly that's how my scooter's headlights worked initially. The headlights died completely after a short period - so I did a
modification with relays to get the head lights work properly. So at the moment the head lights on my scooter can not be compared with yours.
I think you should rather try 1, 2, 3, and 4 (above) on your scooter to see if it works . To my experience the fact that your head lights do not come on, doesn't mean 1, 2, 3, and 4 (above) should be regarded as "dead".
Good luck.