I have a homemade desk lamp that has two LS-113-TP preheat ballasts driving some regular (not HO) Werker F13T5 tubes.
There is also a center F15T8 tube that was preheat driven as well, but the ballast started to get real loud and unpleasant to work under.
I decided to convert the center tube to trigger rapid start with an RLQ-120-TP ballast, which I kind of like more.

As part of setting up the ground for the rapid start, I decided to properly ground the other ballasts. But a side affect seems that the tubes became much more blink happy.
Before, on a "cold start" I would get one or two blinks and the lamps start. Now the lamps blink 8-10 times before they start. Both "hot restart" or "cold."
The ballasts are mounted about a 1/4" behind the tubes.

Is this normal? I mean it's a nice show, but that can't be good for the tubes.

Grounding the case significantly increases the capacitance from the lamp part of the circuit to the ground. That may really decrease starter's inductive kick amplitude, or change its distribution between lamp ends in the case of a symmetrical choke.

Also, if the ballast is really old, insulation may deteriorate, and earth leakage again can steal some starter kick energy from the lamp.

From practice, I'd say it is not normal behavior, but I mostly mess with higher voltage 230V lamp circuits.