It might be that the timer when OFF "lets through" a lot more current than is norma for similar timers and controllersl. The fact that the web site mentions a 4 uF power factor correction capacitor is a big hint that the let through current has to be high. The flash rate of what is quite a large LED supports the theory the let through is high.
The is a let through current as there has to be some current through the timer when OFF in order to power the timer's electronics.
If capacitors cannot solve the problem and the timer is not defective then it maybe necessary to use relay to provide a clean break switch for the LED but the relay coil may not allow the necessary let through to power the timer.
When I search for a 4uF capacitor they all seem to be "motor run capacitors". Will this work?
My local Maplin has a 3uF Motor Run Capacitor http://www.maplin.co.uk/motor-run-capacitors-440v-30309 or a 4.7uF "Audio Grade" capacitor http://www.maplin.co.uk/audio-grade-polypropylene-axial-capacitors-393 Will either of these work? or am I now thinking way too far outside the box. LoL.