to start
YouI believe you have correctly drawn out a viable table with everything you need and yet seem completely at a stand. I can't argue with it. But it appears you need help with k-still, unable to move beyond the tablemaps. So let's get going on that.
RED k-map
I also don't see how you can say "I've also tried making KMaps of the current table but yielded no results". Yet, for example, theThe k-map for the RED LIGHT is simpleprobably easier to see and make from your table:
\$\quad\quad\quad\quad\quad\$ 
Did you produce this, too? I can't tell because you write nothing at all about what you tried.
GREEN k-map
Here's theThe k-map for the GREEN LIGHT is only slightly harder to see by eye:
And here'sBut you know that it must only the case for \$\overline{S_2}\: \overline{S_1}\: \overline{S_0}\$, too, because of how you designed things. So it's not difficult to work out the above k-map from that knowledge.
Here's the newly modified circuit to include that light:
RED k-map you produced
I'llBut let's stop herefor a moment and look at what you actually produced for your RED table (newly updated in your question -- thanks):
It's not correct. You need to write details aboutI'm not sure how you created your progresstable on the left side there. What didBut you getmissed a lot. Do you see how it is really just \$S_2+S_1 S_0\$?
(This is just doing it by eye. But it's also not hard to see.)
automated tool
Perhaps you would like to use an automated tool for this work, instead?
Let's take a moment's break and grab up a copy of Neemann's Digital.
Then you may access the k-mapfollowing service it offers:
This will pop up a starter dialog for you that looks like this:
Right-click on the REDtitles to change them (note that using an underscore in the name causes the following text to appear as a subscript):
Then add another input variable:
Unfortunately, GREENthis adds it to the end of the current list (and gives it a default name, which you need to rename as well.) So move it to the front:
Now rename the output column Y to RED and YELLOW lightsadd more output columns:
Your table might now look like this:
At this point, forstart marking the values in the output columns. For example?, this is what it looks like when modifying the GREEN column to make it a 1:
When done, you writeshould have the following table completed:
Then select the k-map option:
Then you can work through that to find:
This is a little more nuanced than what I produced above, as it includes the "the behavior was nowhere near the expected",don't care states for state 7.
If you now use the following table service:
It will generate the logic for the above in a separate instance of Digital:
On the left side above is what behavior didDigital generated, directly, using AND/OR logic.
Clearly, also, the inputs will instead be coming from the D FFs you get thatalready know you didn't expect? What didneed to set up. So on the right side I've added those, by hand.
summary
At this point, I think I've carried you tryfar enough along. You should be able to getgenerate your own table for creating the unexpected result?inputs needed for the D FFs.
I would suggest that you play with some of the other options you have available in Digital, too. I've only touched upon a few of your choices. for example, Digital will generate CUPL or JEDEC code that can be used to program a GAL16V8! Explore.
