What lamps have more long hot restrike? Mercury lamps (Mercury vapor and metal halide) or high pressure sodium lamp?

Mercury lamps have longer hot restrike than high pressure sodium lamps. New HPS lamps usually have several seconds restrike time for the lower wattage lamps to one minute for 600-1000W lamps, but as they ages and gets redder, their hot restrike gets longer. Mercury lamps have usually 3 mins hot restrike for the 125W lamps and lower, to 7 mins and more for the 400-1000W lamps.
Low pressure sodium lamps have instant hot restrike, except 135W and 180W when operated on autoleak transformers.

Probe start metal halide can take up to 20 min to re-strike, pulse start metal halide can take up to 8 min, mercury vapor is in the 10 min range but longer as they age, some thing that also extends the re-strike time is the fixtures ability to cool the lamp, the faster the cooling the faster the re-strike.

If you need a fast re-strike you can also get a hot re-strike igniter for pulse start metal halide and they come on almost instantly once power is restored but you also need gear rated for hot re-strike because it uses a much higher voltage pulse to make that happen which can damage standard equipment or cause it to fail.

If you have power issues causing the lamp to drop out ( turn off ) you can get ballasts like a SCWA (super constant wattage autotransformer) which will take up to a 45% drop in input voltage before the lamp turns off to help avoid questionable power input common in very remote areas or areas with unreliable power grid so on a 120 volt system that is 66 volts and on 240 it's 132 volts before the light turns off but they are only found in pulse start Metal halide type ballasts and HPS that I know of..

With HPS you can get a dual arc tube lamp which will turn on instantly as well and they don't need any special gear or changes you just screw in the lamp, on a plus if you don't need instant re-strike they last about 40,000 hours.

But if you are just turning the light on and off you might have to wait for it to restart, and if you need constant light and doing it to save power you might want to look at just dimming the lamp (yes they can all be dimmed if you know how, to reduce power usage)

I don't think micole66 is an american member, based on several of his pictures, that showed non american lanterns.
The hot restrike time of high pressure sodium lamps and ignitor operated (Pulse start) metal halide lamps, are strongly influenced by the the ignitor quality. European and british ignitors tends to hot restrike the lamps much faster than the american and several of Eltam ignitors. Several can restrike pulse-start metal halide lamps within 2-5 mins only. Low frequency pulse ignitors (Such as the Israeli made Eltam ES-50), chinese ignitors, tends to restrike pulse-start MH lamps from 10 to 20 mins and more, and it seems that the american gear also tends to restrike pulse start metal halide lamps, after much longer time than the european ones.
Self starting high pressure sodium lamps, often have very long time hot restrike, since the internal starter needs time to cool down before it can fire again (Either the starter itself, as in the case of the british GEC Solarcolour SON-I thermal snap starter, or its thermal disconnector in the case of glow starter or FEC ignitor).

Dor123 I was giving them worst case times, so those times are based on a few things like, they are older lamps and the lamps are in a fully enclosed fixture in a warmer environment like a high ceiling and no air conditioning, now if they have an open fixture outside on windy day when it's -40 the times can be down to under a few seconds, even with american equipment, my 35 watt CMH (Ceramic Metal Halide) lamps at home are all under one minute re-strike with old magnetic advance ballasts (71A5005P) and stock igniters (LI533-H4) but the lamp is in an open fixture and even the cheap HPS wallpacks startup in under a minute and its pretty rare today to play with a self starting HPS well at least I don't see many of them..

For the SON lamps, everything 150W and below restrikes usually in less than half minute, and often instantly. Sparse pulse ignitors like the ES50 tend to take a little longer than ignitors that pulse at the line frequency, but even they are not too bad

In contrast, some 400W..1000W Quartz MH lamps can take 20..40 minutes to restrike