My point is that if the "1st account" and the work you do with it qualifies you for trader status...why worry about any other trading account ?
Account titling matters.
An entity can have TTS, just the same as an individual. An individual and an entity are not the same to the IRS. And there are retirement accounts, for the benefit of an individual which likely falls under the TTS qualification for the individual, but there are exceptions for sure, for instance a trust. Keep in mind too, that TTS does not allow co-mingling of "investment" and "trading" accounts and/or trades for tax purposes. Seek professional advise for clarity.
I doubt the OP has this type of complexity but we don't know. In which case, the individual qualifies for TTS or not. And as you've pointed out, the number of accounts is irrelevant.