Suppose you have two exogenous latent variable. (There will be directed paths from them to a response variable.) Is the covariance between the two exogenous latent variables part of the model? That is, do I have to include a path specification for the covariance or otherwise the covariance will be constrained to zero? I understand that the covariances among exogenous manifest variables are not part of the model.

If you're talking about RAM, then there's no distinction between exogenous and endogenous variables, only latent vs manifest. The term exogenous is a bit of a misnomer for LISREL, but it's in common usage. LISREL has a covariance matrix for its exogenous latent variables; it's called Phi. If you don't specify paths in Phi, then they are assumed to be zero. So definitely model them if you think they are there.

Stands up on soap box.LISREL has exogenous and endogenous latent variables. The manifest variables are just indicators for these latent variables. Accurately, they should be called the indicators of the exogenous/endogenous latent variables rather than exogenous/endogenous manifest variables. According to path tracing rules, all the manifest variables in LISREL are endogenous because they all have paths going into them: the factor loadings paths. MPlus, on the other hand, has only endogenous latent variables, no exogenous ones. But it does have endogenous and exogenous manifest variables. As far as I know, there is no modeling framework that has (1) endogenous and exogenous latent variables and (2) endogenous and exogenous manifest variables. LISREL has (1) with endogenous manifest variables. MPlus has (2) with endogenous latent variables.Steps off soap box