The large-scale forecast for Monday seems to be stabilizing, but I still consider highly specific cloud forecasts to be difficult given the weak large-scale forcing. A high-amplitude ridge parked over our area would be a godsend for forecasters, but that's not what we're looking at for Monday.
Instead, the GFS calls for a weak upper-level shortwave trough to sweep across Idaho and Wyoming from 1200–1800 UTC (0600–1200 MDT), and be accompanied by some mid- and high-level clouds. A short-wave ridge further west builds along the Pacific Northwest coast.
Eclipse time is approximately 1721 UTC (1121 MDT) in Redmond, OR, 1730 UTC (1130 MDT) in Stanley, ID, 1736 UTC (1136 MDT in Jackson, WY, and 1741 UTC (1141 MDT) in Riverton WY. That's just before the bottom image above, which given the GFS forecast would yield the lowest cloud cover odds and fractions during the eclipse over eastern Oregon and increasing cloud cover odds and fractions as one moves eastward to western Wyoming.
The NAM agrees with the basic synopsis being advertised by the GFS, but note that the shortwave trough orientation is more from SW to NE (positively tilted in meteorological vernacular, and that the structure and characteristics of the clouds varies when one examines the gory details.
That variation in the structure and characteristics of the clouds represents the dilemma for forecasts along the path of totality over Idaho and Wyoming. This is a weak shortwave trough, so a routine "public" forecast would be pretty straightforward. Probably mostly sunny given the fact that some mid and high level clouds aren't going to be a big deal.
However, exactly where and when clouds will be at the time of eclipse is difficult to ascertain. Will one have a clear view of the sun in Jackson, but have an untimely patch in Driggs? Impossible to say. In part, this reflects the unpredictability of such cloud cover at such long lead times, but also the fact that present day forecast models do not explicitly resolve cloud processes, adding to the forecast uncertainty. Timing will also matter. For example, if you just happen to be underneath a local area of clouds at the time of eclipse, that's a bummer.
Based on current forecasts, the greatest likelihood of clear skies over the interior mountain west eclipse path is eastern Oregon. The potential for some mid or high clouds exists as one moves eastward, especially over eastern Idaho and Wyoming. The timing, location, and extensiveness of that cloud cover remains uncertain.
For your planning purposes, here are a few products for your consideration:
1. NWS Digital Forecasts. You'll need to use the drop-down menu to request "Sky Cover (%)" and select the appropriate time. 12 PM is the closest available. One disadvantage of these forecasts is that they are "deterministic" and don't show the full range of possibilities. Numbers represent percent of cloud cover.
Keep in mind that even at short time scales, errors in cloud cover are to be expected. Use the HRRRX (and other model forecasts) as guidance, but not absolute truth.
3. GOES-16 Imagery. I'm a huge fan of these high-frequency, geocolor loops from CIRA. Use for "eclipse chasing" the morning of the event and fine tuning during the event, if traffic permits.
Hopefully, the forecast verifies with minimal clouds and not an unfortunate veil of thick cirrus. Good luck!