Quote from tc5:
I am not an FX expert, but...
Yes, the TA for the currency pair A/B you are trading would obviously be of primary importance. The TA for pairs involving involving A or B would be of secondary importance. The TA for pairs not involving A or B would be of tertiary importance.
Of course, analyzing each additional pair would be a lot of extra work if you did it the same way as you do for the primary pair (e.g., using the technical analysis that most people do)... unless you did it with much less scrutiny than for the primary pair.
If you are trading EUR/USD, then of course knowing what EUR/GBP and GBP/USD (and even JPY/GBP) are doing would give you extra (marginal) information.
You could summarize the set of all pairs you want to consider by looking at the matrix of rates and the correlation matrix. What would be cool is doing TA on those matrices.
In fact, I'm sure there are people out there in quant FX shops and individuals who do relatively sophisticated statistical analysis on the correlation matrices of currency pairs along with other information.