What more could be learned from a rare astronomical event if we knew precisely when it would occur? This is actually related to a question I recently asked on Worldbuilding, but seemed more appropriately asked here.

To keep this from being too broad in scope, let's assume that someone figured out the exact moment that Eta Carinae will go supernova (I wouldn't hold it against anyone if they suggested a more scientifically interesting event).

Due to this foreknowledge, we could point every telescope we have in its direction for the main event.  Is there any science we know we could do/learn from this event that we wouldn't get by reacting to it after the fact?  I know such an event would generate data for a century or more to come, but I'm interest in the moment of the explosion.

Somewhat related, is there anything we would/could do now to prepare for it if this event were going to happen today?
I would argue that simply knowing that a star was about to undergo a supernova could be information enough.

It's not always easy to figure out what type of star a given supernova progenitor was. Sometimes, there were no observations of the relevant region of sky prior to the supernova, and so we can't simply look back at prior observations and extrapolate from that. We can definitely look at certain spectral lines and other information from the remnant, but it's rarely as sure as actually observing the progenitor.

There are some classes of stars which have yet to be conclusively identified as supernova progenitors, though there may be evidence suggesting that they should evolve as such. Red supergiants are one group, leading to the so-called "red supergiant problem" (see Smartt et al. (2009) and this question). If we knew that a red supergiant was a supernova progenitor, that would possibly solve the problem.

Wolf-Rayet stars, thought to produce Type Ib/c supernovae, are another group (see Yoon et al. (2012). Evolutionary models and indirect observational evidence predict that they should lead to these supernovae, but no observations of Wolf-Rayet supernova progenitors have been observed.

Eta Carinae A - which I assume is the star you're referring to - appears to be a luminous blue variable (LBV). We do know that LBVs lead to supernovae (see for instance the case of SN 2006jc, which underwent a major outburst two days prior). However, it can be harder to distinguish between supernovae and certain supernova imposter events, caused by LBVs. I'd speculate that we could try to observe Eta Carinae A in the period leading up to the supernovae, to try to observe the differences between outbursts and the actual supernova, which could give us better information on the nature of the evolution of these stars. Additionally, there is neutrino emission in the periods leading up to supernovae (see this question); perhaps detectors on Earth could monitor the progenitor and see if they can find anything.

We could also, given enough warning time, attempt to study the progenitor in the final phases of stellar evolution. This page gives a table for the time periods of various fusion phases in the life of a $25M_\odot$ star:
$$\begin{array}{|c|c|}
\hline \text{Fusion phase}&amp;\text{Length of phase}\\
\hline \text{Hydrogen} &amp; \text{7 million years}\\
\hline \text{Helium} &amp; \text{500,000 years}\\
\hline \text{Carbon} &amp; \text{600 years}\\
\hline \text{Neon} &amp; \text{1 year}\\
\hline \text{Oxygen} &amp; \text{6 months}\\
\hline \text{Silicon} &amp; \text{1 day}\\
\hline
\end{array}$$
This would let us figure out where the star is in its life and figure out what effects different fusion pathways could be having, if any.

Finally, I'm assuming that your question means that we know when the light from the supernova reaches Earth, and that this would happen in the near future.