You have 3 options for neon flashers. 1 is to have a transformer per sign, and a sequencer to switch the primary side supply, using either an electronic solution with a slow oscillator using a 555, a 4017 and a few MOC 3064 opto triacs and BT157 triacs for current boost with zero cross switching. 2, you can also use a Faraday motor, which works off eddy current in a metal disk, which turns an eccentric cam which operates 3-6 very large switches which then switch the transformer primaries. 3 is to use high voltage switches, but there are only 2 options, a very expensive high power reed switch, rated for 20kv and 500mA ( and at $400 each last time I looked, with a limited life) or a geared motor running what is essentially a motor vehicle distributor to switch the spark.
The primary side switch is the most common, it is always going to be cheaper to use an unswitched high voltage side, and simply switch the transformer. This is very reliable, the neon transformers I have are a mix of old and brand new, the old ones having done multi decade service up in a sign, switching at 30 flashes a minute 24/7/365, and there the most common failures were neon breaking from thermal shock or vandalism, or the electronic controls dying from wear. Simple modules, but as they were potted they were not repairable, as the potting used was non reenterable. I have a homopolar switch from an older sign, still works, but as it was a 4 flash instead of a 3 I did not use it.
High side switching is also discouraged as it generates a lot of very high power broadband noise, as it is essentially a spark gap transmitter, and with up to 150W of power, it is very powerful and is going to cause interference from the LW broadcast band ( 60kHz) to well in the gigaherts band.