How about this:
we know that
the Californian's 7.30pm star sight was 42.05 N. We also know that the current that night was 0.7 knots to the SSE.
Now, taking the N-S distances only, to make the sums easier (!)...... when
the Californian stopped, she was at 42.05 N, but this doesn't, I believe take account of drift. If we assume, probably incorrectly!, that the drift started straight after 7.30pm, then this will mean that the Californian stopped for the night 1.983 miles south of where she thought she was (since she stopped at 10.21pm). By the time the Titanic collided with the berg, she would have drifted another 0.933 miles south.
The Titanic's stern section is at 41.44 N, and this is after 2 hours 40 minutes of drift, so she possibly started at a point 1.86 miles to the northward. So, therefore, all these assumptions being correct, the 11.40pm Titanic-Californian distance would be 16.22 miles N-S.
So, could the two ships have seen each other?
The Californian's sidelights, at a height of 49 feet above the water, provide a range to the horizon is about 8.0 miles.
From the Titanic, the height of the sidelights above the waterline would be 60 feet, or range to the horizon of 8.8 miles. So, the total possible didstance to the horizon would be 16.8 miles, which means that anyone inside this distance would see the other ship's sidelights.... note that this does not include how faint the sidelights would seem from the other ship - it may be that they were too dim to be seen at that range.
If Gill's account is to be believed (and I for one don't), then he was watching the other ship (which he didn't see) firing rockets at 12.45pm-ish. Now, he was several feet below the bridge where Stone and Gibson were watching the ship and rockets. It may be that Gill was just too low down, and below the horizon to see the other ship. "His" range to the horizon can be calculated if someone can tell me where his vantage point and his height above the waterline. I guess he'd be watching from the well-deck, or perhaps f'ocsle or poop.
It also means that the flares fired by
Boxhall would be below the range of the horizon and hence, not seen.
Paul