Found cointegrations - should use OLS/cointegrating vector?

[Allnames]

Hello,

As my title suggests, if I don't find cointegration by Engle-Granger approach (using OLS) but I do find cointegration using the Johansen approach. What should I use as my long-run relationship?

As definition of cointegration, OLS is fine. But the two, OLS coefficients and cointegrating vectors, are absolutely contradict each other in terms of the signs. (OLS gives my expected signs, but cointegrating vectors give the opposite)

I am quite worried about my understanding. Can anyone please have me clear out this confusion.