Univariate EGARCH can't be extended to bivariate case in EViews by Wizard unless there is a special code developed by someone. The best software for this model is RATS. You may also want to check 'rmgarch' package in R.
Neither univariate not multivariate EGARCH has an underlying stochastic process that leads to its derivation, no regularity conditions, no likelihood equation, no Jacobian or Hessian matrices, and hence no asymptotic properties of the QMLE.
In short, EGARCH has no statistical properties.
It might be useful to read the following short papers on EGARCH:
“A one line derivation of EGARCH”, Econometrics, 2(2), 2014, 92-97.
“The correct regularity condition and interpretation of asymmetry in EGARCH”, Economics Letters, 161, 2017, 52-55.
“On the invertibility of EGARCH(p,q)”, Econometric Reviews, 37(8), 2018, 824-849.