I just beat the Elite Four and Gary last night, with the in-game timer at almost exactly 13 hours. I'm actually a bit surprised it took me this long, as I've been able to power through the recent Pokemon games in less time. I forgot how many and how detailed the "dungeons" in RBY are, and I guess the world sizes haven't actually increased that much over the generations. Plus I wasted so much time managing items because my computer and bag got full.
I solo'd the whole game with my starter Pikachu, which probably wasn't ideal, but it wasn't that difficult. I grinded before Brock until Pikachu learned Double Team at level 15, then abused that for the win. It was surprisingly easy (or maybe I got lucky). Giovanni (at Viridian) gave me way more trouble. While Pikachu could take a few Tackles from Brock's Geodude and Onix, it could only take two Earthquakes from Giovanni's Dugtrio, Nidoqueen, Nidoking, and Rhydon. I abused Double Team again, but also had to use two hyper potions to stay healthy. I also taught Pikachu Seismic Toss (TM19) to have a reliable damage-dealer for ground types. It was able to KO almost everything in 2 hits, other than Lance's Dragonite and Gary's Sandslash, which took 3 hits. Pikachu was level 79 going in to the Elite Four, and level 82 after beating Gary. So if you're thinking of solo-ing Yellow with Pikachu, that's how I did it.