I'm not familiar with the viscosity of tenacious oil, but I doubt it is too thick. This works to get a minimal but sufficient amount of Pro Link into my chain rollers. On a nappy washcloth (thick nap holds oil well) soak a spot about 1" in diameter. Hold it up against the rollers and rotate the chain slowly. Do top and bottom. Capillary action will take it into the rollers. Wipe the sides of the chain clean with a dry part of the cloth. There shouldn't be any excess.
Run your finger back and forth along the length of the chain on the rollers. You should be able to feel well lubed rollers turning smoothly. After a few rides, run your fingers along it again. You'll know when it's time to clean/lube again. bk