I haven't shot 16mm with neon tubes, but you do need to be a bit careful as to flicker. There's essentially two options for driving them: older installations will use big iron ballasts, which look like a chunky transformer. These have essentially the same flicker considerations as any gas discharge light, such as an old fluorescent, mercury vapour industrial lighting, or ceramic metal halide; they'll flicker at the local mains frequency (60Hz in your part of the world.) Mitigation techniques for this are widely publicised. More modern displays may use electronic ballasts which may not flicker, or which may have complex flicker characteristics; all you can do is shoot tests. Any such effect should be visible in the viewfinder of a running, unloaded film camera, but there is probably very little you can do about it.
In my very limited film experience, neon tubes render fairly well on film since it retains colour better in bright hilights - but the only true neon tubes are the clear glass red types. Anything else is actually an argon-mercury tube with a coloured phosphor coating. Bold colours tend to end up roughly where they started but the whites can misbehave in exactly the same way as an old-style fluorescent; don't rely on them looking white. Again, it's hard to predict what will happen here, so if it's crucial that you render a piece of neon with accurate colour, you'll need to test.