It’s possible to fit daytime running lights to a XK8 or similar for just a few pence (well, a couple of quid). There is a wonderful series on YouTube called “To the garage” and in one of these there was a link to a light upgrade for XK8 cars.
One simple approach is to get the fog lights, which are standard, to come on as daytime running lights. Easy to do with one diode.
You then push the diode in between these two relays in the right tang position. The diode gets trapped when you push the relays back in place. This has the effect of turning on the fog lights with the ignition and, when you turn your headlights on, the fog lights go off just like daytime running lights. This works with high beam and low beam, as low beam stays on when you switch to high. If you want the fogs on with the headlights, this works as normal by pressing the dash button. The only thing you will notice is that the fog light indicator is on when driving at all times until the headlight goes on.
The pictures show the position and orientation of diode. The latter is important because current will only flow one way in a diode. It’s a 3A-rated diode which is way more than the load at the relay; the main part of the relay takes the current, while the diode just needs a small current telling the relay to switch on.