The thick red one is live all the time, if you put a meter across it now, you will see +12V.

The way I initially said of doing it would mean the button would only work with the ignition switched on BUT I would not advise it as it may pull to much power from the ignition (Pos 2 circuit) so as always with any advise on a forum, you do so at your own risk!

The black usually denotes a switched live, so this could be the ignition circuit, you can easily see by putting a meter on the wire with the ignition switched on, if you have power then it is the ignition feed, and the remaining wire is the remote starter wire.

Martin