Well, I have to say Felix got the answer as the never-seen sponsor was Rothmans indeed! I found a source about this in a Japanese magazine some months ago along with illustrated Rothmans livery of 019. Another rumor around Tyrrell of this time was that Braun was pretty convinced that they're going to sponsor McLaren instead of Tyrrell right until the moment of 020 unveiled, as McLaren was doing marketing stuffs for Tyrrell.
This is the article I've mentioned, the text itself is by Alberto Antonini but I'm not quite sure whether this have been revealed in English sources. The illustrated Rothmans-Tyrrell is just a reference of a story that might happened, I don't have the source of what the actual colouring was like. The rough translation of what article says:
[One of the most interesting side stories regarding Tyrrell 019 might be the one with its colouring. The Blue-on-white livery on Tyrrell in 1990 was almost as striking as its high-lifted nose cone, being elegant and also sporty at the same time.
However, this livery was designed for a title sponsorship that eventually never became real. Jean Claude Migeot knows the whole story: ''There's only few in the team know this, including me, that the initial colouring design consisted of a Rothmans logo on the blue portion. We were going to get Rothmans as title sponsor in 1990. Sadly the deal eventually fell apart, which was not a rare case in Tyrrell at the time: We even had the document prepared, but nothing do happen at the end of the day."
Rothmans logo was never seen on Tyrrell's Grand Prix cars (four years later Rothmans brought their budgets into Williams team), but Migeot went on with the original colour scheme anyway. "The main reason was that I loathed the classic Tyrrell dark blue, for it being very monotonous and uninteresting. I always looked for something new even in term of colourings, and with that livery the car looked so smart and elegant, so we went on and stuck with the plan."]
So it's your turn Felix...