The GI circuit runs 6.3 volts AC at 60 HZ, so any LED bulbs in the GI circuit at full brightness will spend 1/120th of a second illuminated and 1/120th of a second turned-off. It is similar for all other circuits that use lamps because they were all intended to use incandescent bulbs (and thus use alternating current).

The frequency of the AC circuit is causing your flickering because your LED bulbs are most likely nothing more than an LED with a 47 ohm resistor in-series inside the casing. This problem can only truly be solved by using a bridge rectifier and a smoothing capacitor to convert the AC current to DC current, but this can be a bit of a bear to deal with for someone who doesn't know what they are doing.

However, there are sellers that sell LED bulbs with a small capacitor that helps relieve bulb flickering. Shoot some emails to Cointaker.

I was assuming he was using the cheap ones you speak of.

Sorry, I should have payed more attention to the posting. But in the case of the matrix, it's oscillation can still be smoothed with a capacitor.

I didn't realize it was that slow. I did a similar project on the black translite sockets and assumed that the frequency was at least somewhat close about all the lighting circuits (the manual can be a bit ambiguous). For my project I ended up rectifying the GI current and using a 2200 uF smoothing capacitor behind each socket.

So you're right in that caps would have to be soldered in below the base.