Ok, I ended up buying 2 timers and I thought I could get them installed in the same receptacle as shown in the attached photos.
It turns out, I had 2 more travellers wired in to this box which severely limited the space available.
Firstly, the fuse box in the basement did not have this circuit marked. It turned out there was one live line heading to this switch (for the 2 kitchen lights) and then a couple of more travellers that spliced in to this live line which powered the living room lights and plugs and basement switch/light.
So in the box I had 1 LIVE line heading to the fuse box (black/white/copper).
2 lines that were not live (black/white/copper), but spliced in to the 1 LIVE line and used to power the rest of the 1st floor.
Those 3 lines had all the blacks joined, all the whites joined and all the copper connected to the box ground.
As for the actual kitchen light, one of the live blacks (spliced in to the LIVE) also went into one end of each of the switches, and they ran a 4-line cable (black/red/white/copper) up to the kitchen ceiling which formed the loop to the other end of the switch. The black of this 4-line cable went to the other end of one switch, the red went to the other end of the other switch (to control each light separately) and the white of course spliced into all the other white neutrals common to both travellers and the live line (the one connected to the fuse box), and the ground attached to the copper ground.
Due to the lack of space in the box, I had to make the timer control BOTH of the kitchen lights, so I combined both black/red of the 4-line to the timer. The other switch now does nothing. The timer can handle 1800 W max and my kitchen lights are 35W CFL's so even both combined are well under.
As far as what I discovered upon entering this switch... I wonder if this is a normal way of wiring things. There was absolutely no space in this box, I barely managed to fit the timer, let alone all the connections which the electrician decided to use this area for to connect up all the travellers to the other plugs/lights on the first floor. Plus the fact that none of it was labelled, neither the fuse box, nor the light switch itself (see the photos). I had to figure it out using a multimeter.
[EDIT: Sorry I may have some of the terms wrong... not "travelers", I think I am using this incorrectly. It is just circuits that hook in via parallel connection and just happen to use the box that also has the wiring for the lights]