Just searched for illustrations of peak when lamp is ignited and found this (about fluorescent tubes but similar peak applies to HID also):
###Fluorescent tubes
The theoretical peak current at switch-on can therefore reach 27 times the peak current during normal operation.
There is therefore a risk of contact welding in electromechanical control devices (remote-control switch, contactor, circuit-breaker) or destruction of solid state switches with semi-conductors.
In reality, the constraints are usually less severe, due to the impedance of the cables.Source: http://www.electrical-installation.org/enwiki/Electrical_characteristics_of_lamps
##hid Lamps electrical properties
Mercury and high pressure sodium lamps can easily take twice the normal current during warmup, although most ballasts do not provide this much. In my experience, mercury lamps can take 2.5 to probably 3 times the normal operating current during warmup. High pressure sodium lamps can take even more, at least 3 and usually 4 times the ratio of nominal wattage to nominal arc voltage during warmup (in my experience) as long as rated wattage is not exceeded by more than 15 percent.
Source: http://www.lightingassociates.org/i/u/2127806/f/tech_sheets/hid_lamp_electrical_properties.pdf
And one more HID measurement:
So please count (for correct Amps) with switch-on peak when choosing your timers!