It's hard to prove some information doesn't exist, but maybe I'll get points for effort ;)
There is a section on "Post exposure vaccination" in the (long) World Health Organization Background Document on Vaccines and Vaccination
against Tick-borne Encephalitis (TBE). They mention the concern you also cite in your question, but go on to say that there is no evidence for it:
Of special concern is the theoretical possibility that post-exposure
prophylaxis could result in antibody-dependent enhancement of the infection and exacerbation of the disease. Such phenomena have been reported for other flavivirus infections, but not for TBEV.
At least, vaccination after exposure will probably not fast enough to prevent an infection (vaccinating after exposure is, for example, done for rabies):
Since TBE has a relatively short incubation period, even an anamnestic response may not be fast enough to protect the individual following exposure.
This information all seems to come from the review After a tick bite in a tick-borne encephalitis virus endemic area: Current positions about post-exposure treatment. It is also repeated in the WHO position paper Vaccines against tick-borne encephalitis.
Neither those studies nor the manufacturer information for FSME Immun (which might be what you would receive - warning for others: that information is in German) state a waiting period. A good guess would probably be the incubation period for TBE (median 8 days).
That part is easier. For the two vaccines usually used in Western Europe, the WHO writes
With both vaccines the manufacturers recommend a booster 3 years after completion of the primary series and subsequent boosters at intervals of 5 years (3 year intervals for individuals aged >60 years)
See table 6 on page 43 of the Background Document on Vaccines and Vaccination against Tick-borne Encephalitis (TBE)
As for scheduling, even after those 3 or 5 years, protection is still really good (after 8 years, 90% were still protected), so there's probably no rush and the booster can be taken when convenient.