I've seen Brocken spectres quite a number of times - they are much more common than you think once you know where to look. There isn't really a best time of year. Relatively high pressure is the thing, when clouds could be trapped low in the valleys and there is sun above.
You need to be near the edge of a steep escarpment or cliff, with the sun in the opposite direction from you as the cliff, so that your shadow will fall over the edge. This is hard to acheive if the sun is high in the sky; in the morning or evening when the sun is lower your shadow is also longer so this is the best time of day to see them. Once you know this, then whenever there's a temperature inversion - not that rare - you can work out where you need to stand and when in order to see your 'spectre'.
Good luck!