The Milky Way's central supermassive black hole (SMBH) is feeding, albeit at a very low level. Radio emission from the accretion disk (and/or weak jets) is responsible for the long-lived "Sgr A*" radio source.
Here is a paper from 2000 (Falcke et al.) arguing that VLBI (as used by the Event Horizon Telescope) should be able to image the "black hole shadow", based on the known sub-mm and mm-wave emission. And in fact the EHT has been observing the Milky Way's SMBH.
As I understand it, the real reason we haven't seen a formal, published detection of the Milky Way's SMBH by the EHT is that its emission is highly variable on short time scales (e.g., minutes to hours). In the case of M87's SMBH, the variability of the (sub-mm and mm-wave) emission is slow (days to weeks), so they could combine observations taken over several hours and two nights in April of 2017 under the assumption that it was all of the same static configuration. Figuring out how to properly account for the short-term variability of the Milky Way's SMBH emission is much more difficult, which is why the (relatively) easier case of M87 was solved and published first.
See also Rob Jeffries' answer to this physics.stackexchange question.
Edited to add: Unfortunately, I don't think there's any validity to the idea that we can track incoming "food" and predict future accretion flares for the Sgr A* SMBH with any useful accuracy. There was some excitement a few years ago when a group reported detection of an apparent gas cloud ("G2") on an orbit that would take it in to about 2000 Schwarzschild radii from the SMBH at pericenter (in 2014), possibly allowing it to be tidally shredded and increasing the accretion rate. But as a review article published in 2013 pointed out, "The actual free-fall time scale from ∼2000 $R_s$ is roughly one month and the viscous time scale could be anywhere between months up to hundred years depending on the viscosity parameter $\alpha$."
And in fact the actual pericenter passage produced... nothing much at all. There's a discussion of the "fizzle" here: "with the majority of the simulation parameters used, only 3–21% of the material Sgr A* accreted from 0–5 years after periapsis is from the cloud".
So in the one case where potential "food" was identified and tracked, one couldn't be sure in advance whether the possible increased accretion would happen on timescales of months to years, and so far nothing significant has happened. I very much doubt the EHT team is basing their observing schedule on this kind of thing.