I remembered that I had a Sauerkraut factory that I'd gotten in a trade and have no plans to use. I popped it's circuit into the Amtrak just to get the regular lights going. Works silently. It's a simpler circuit with only a three part animation on one sign though it does have a rate knob which the Amtrak does not.
Sauerkraut circuit
Amtrak Circuit
Next up to try and figure some way to chain the Amtrak signs into an always on configuration.