Reddish brown sounds a bit like rust contamination, not totally unheard of in the primary chain case due to condensation. There is a long explanation of this phenomenon on this forum somewhere, I would search Hugo Myatt, basically the engine can pressurise the chain case through the main bearing, and the pressure in the chain case forces oil into the gearbox, I am not for one minute saying this a definitive explanation of your problem, but perhaps something you should consider, if that does prove to be the problem, I have to tell you there is no quick fix.
“Is it possible for engine oil to migrate to the gearbox?” Under certain very specific conditions the answer is yes. This happened on my Rapide about twenty years ago. A quick but not infallible test is to temporarily fit a D type breather cap, or some other large bore breather to the primary chaincase. If, on riding the bike, the oil level in the gearbox ceases to rise but the level in the primary chaincase rises the following saga may be of interest.
The whole saga was recorded in MPHs 561 to 569 and also in “Another Ten Years.”
My Rapide engine had recently been rebuilt by a renowned and much-lamented Vincent expert. He had incorporated many subtle and successful modifications. Unfortunately, there was a “Market Garden” syndrome in that there was one modification too far, but back to that in a minute.
There had always been a slight oil leak from the dynamo drive and I went to a great deal of effort to completely seal the drive. In this I was completely successful. With the standard filler cap fitted the primary chaincase was completely leak free. This is when the trouble manifested itself.
After riding the machine, I checked the oil level in the chaincase. Horror! There wasn’t any! However, the oil in the gearbox had risen rapidly.
After a great deal of investigation, frustration and consulting all sorts of experts I eventually discovered what was happening. The final mod the re-builder had incorporated was to use a sealed bearing in place of E91, the outer drive side main bearing. This bearing had the inner seal removed leaving only the outer seal in place. He also dispensed with ET 77, the reverse oil scroll spacer and replaced it with a plain spacer. The unfortunate result of this modification was to make the half-sealed bearing an exceedingly efficient ‘’flap valve’. As the pistons descended this forced engine oil into the chaincase whilst pressurizing it at the same time. When the pistons rose the ‘flap valve’ shut off equally efficiently so trapping the added pressure in the chaincase. This meant that the pressure in the chaincase rose exponentially with every movement of the pistons and having nowhere to breathe the chaincase oil was forced to escape the only place it could – through the gearbox mainshaft oil seal into the gearbox. The gearbox oil seal is designed to prevent oil from leaking out of the gearbox and not preventing chaincase oil, under extreme pressure, entering the gearbox.
Sadly, the only cure for this was an engine strip down and a reversion to the standard arrangement for the drive side main bearings, that, and less than total sealing of the dynamo drive.