Okay, time for a follow-up on this one.

I have been fiddling with this for a long, long time and finally figured out what was going on. My electrical installation is leaking a tiny amount of current, which is causing a small voltage to be present even if it is switched off because a regular switch only disconnects one wire. This is not a Powerbar related issue per sé, it is also on the digital timer I used. This current seems to be charging a capacitor in the power supply which discharges when it is full, causing the flashing of the LED lamps every so many seconds (120 in my case).

To solve this I have purchased a special timer which disconnects both '+' and '-' when switched off and voilà, problem gone.