The push button switches have special plugs. It helps to get the plugs with the switches if you can, complete with a few inches of the wires. You can then splice the wires into your loom. The wire colours are generally the same between the looms. If you cannot get the plugs you can re-terminate your wires with the required 4.8 mm crimp on female spade terminals. Use uninsulated terminals and cover them with heat shrink sleeves. Pre-insulated crimp terminals are too bulky to fit. You will have to provide new switch illumination supply and ground wiring as the push button switches have individual globes rather than fibre optics.
The push button setup in the photo is fitted upside down!