Hoping I get this about right.....
Sample data and possible design considerations, single letter beacon transmitting 2 watts RF for one second once per minute
0.074 AH - estimated current consumption
2 - number of cloudy days
5 hrs - minimum the sun will shine during the day in winter
7 hrs - minimum the sun will shine during the day in summer
0.060 Amp minimum current draw when not transmitting
0.300 Amp maximum current draw when transmitting
1 sec transmit time 60 times per hour hour (60 seconds total transmit/hour)
24 hour consumption:
0.06 x 0.9833 x 24 hrs = 1.652 AH (98.33 is the percent of time drawing 0.06 Amps)
0.30 x 0.00167 x 24 hrs = 0.120 AH (1.67 is the percent of time drawing 0.03 Amps)
So 1.772 AH total consumption in 24 hours to be replaced by the solar panel the next day plus supporting normal current draw
On the short days of winter we'd have 5 hours of good light on the panel so 1.772 AH / 5 = 0.360 Amps from a perfect solar panel at minimum
Then 0.36A times 18v equals 6.4 Watts so a 10 Watt panel could work. They typically have a 0.55 Amp short circuit current capability
If we had two cloudy days the transmitter would draw 3.45 AH total so a 7 AH battery might be the minimum size to avoid running the battery flat. Snow on a panel or longer periods of cloud reduce charging capacity.
Typical good quality Chinese 10 watt rigid frame panel on Amazon
https://www.amazon.com/ALEKO-PP10W12V-Polycrystalline-Opener-Driveway/dp/B01N5R81WR/ref=sr_1_68?keywords=10+watt+panel&qid=1550273735&s=gateway&sr=8-68