What is a good reference for open problems relating to the Ramanujan tau function?

I know about Lehmer's conjecture. I know the following reductions of the problem: the smallest counterexample must be a power of a prime (by the multiplicativity of $\tau$), it must be a prime (by considering the linear recurrence expressing $\tau(p^{n})$ in terms of $\tau(p^{n-1})$ and $\tau(p^{n-2})$ ), and it must be a prime $p$ such that $p \equiv -1 \mod{691}$ (this follows from the congruence $\sigma_{11}(n) \equiv \tau(n) \mod{691}$). Are all the other reductions, like the last one I mentioned, just obtained from congruences satisfied by $\tau$?

I have read that problems about the sign of $\tau$ tend to be hard, but I don't know precisely about this (aside from the problem I just mentioned about the vanishing of $\tau$). Where would problems about the sign of $\tau$ be discussed in detail?