The energy-time uncertainty principle is different from the others. Usually, you have observables in quantum mechanics which have some sort of probabilistic distribution, and the normal uncertainty relation is given as
σ*_A_* σ*_B_* ≥ something
where σ*_A_* is the standard deviation of the distribution describing A, and "something" depends on the properties of the observables A and B. ("something" can be zero, where the uncertainty principle just tells you that standard deviations are positive; it can't be negative).
But time is not an "observable" in the technical sense I gave above, because there is no probability distribution for the time of the system, so there's no standard deviation. The time is just a parameter which the probability distributions of all the observables depend on. This basically answers your question: time cannot "tunnel," it doesn't have a distribution and can't "collapse" etc.
So what is the correct statement about the energy-time uncertainty principle? It is the following: Consider any observable (once again, in the sense I have in the first paragraph) B. Now consider the energy, E. The following is true:
σ*_E_* σ*_B_* ≥ (ħ/2)|d<B>/dt|
Here, <B> is the average value (mean) of the observable B. If the average value of B doesn't change with time, then there's nothing interesting to say here. But if B is changing with time, then there will always be an uncertainty relation between E and B.
Let's think about what this means physically. If you have a system where some observable B is changing, then the energy of that system must not be well-defined - instead there is some spread. This must be true, in particular, for any unstable system, since an unstable system is defined as one which is changing w.r.t. some observable. So unstable systems have some distribution of energies which must satisfy
σ*_E_* Δt ≥ ħ/2
where Δt = σ*_B_*/|d<B>/dt| is sometimes called the "time uncertainty." You can think of Δt as the approximate time it takes for <B> to change by an amount σ*_B_*. If this amount of time is large (which happens for stable systems with long lifetimes), then the energy uncertainty is small. Vice-versa, if this amount of time is small (e.g. in unstable systems), the energy will have a very large spread.