'there's a female plug, and a male plug, both marked timer'
The cord from the timer would plug into the female jack.
You would need an extension cord to plug into the timer, and the other end into the male jack.
To emulate this, you need a foot switch that has BOTH a cord to plug into the wall, and a jack where you would plug a lamp into the foot switch. A foot switch from a hardware store that only has a cord going out to a plug that you would sit between the wall outlet an a lamp won't work, it does not have the right electrical connections.
'I have found a Fujimoto 125v 3A footswitch, can I plug it directly into the female plug in the transformer, and use it as a mains switch? '
From your description, the Fujimoto foot switch will not work. It only plugs into 1 of the 2 plugs on the timer.
Be VERY VERY careful when working with electrical stuff.
If not wired CORRECTLY, you could have a dangerous situation.