Are you sure all the other lamps flicker and it is not just the
effect of the one lamp. If every
fixture or multiple instruments on the same
dimmer rack are flickering then you have a significant
current being drawn for a very short time.
As you have isolated the trigger for the flicker and confirmed it follows the
fixture as you move from
dimmer to
dimmer you now need to confirm the problem is the burner assembly by swapping it to another S4 housing assembly. If the fault follows the burner then you should open the plugtop and check the connections inside and make sure they are tight and show no signs of heat damage. If this checks okay swap in a new
lampholder which is a couple of minutes work and costs less than $20. You should also check the old lamp holder/
whip to see if there is any damage to the
insulation. If so look for any signs that this could have been caused by a sharp
edge or a
wire bing pinched, especially under the stress relief on the back of the burner. just because a
lampholder doesn't look damaged doesn't mean it is not internally damaged and you can't see it.
If the fault does not follow the burner then you are looking for something entirely different because you probably have two faults present that together produce the flicker but if only one is present you do not see anything. This is more of a challange but workable.