The 'good deposit' referred to in v14 would most logically be 'the pattern of sound words' that the writer refers to in v13. I don't any reason to look back to a prior sentence to determine what the deposit is.
Maybe the writer is referring back to what was written previously to the same recipient. Look also to 1 Tim 6:20 where we read 'τὴν παραθήκην φύλαξον' (keep safe what has been entrusted to your care) here the writer proceeds to warn his reader to avoid 'profane and idle babblings and contradictions of what is falsely called knowledge.' here then it seems that the writer wants his reader to maintain the 'sound' teachings (knowledge) he has received. The parallel seems clear between these two texts.
The deposit mentioned in v12 is that which the writer has committed to the 'he'. Whilst these two things are both 'deposits,' i.e. things that have been entrusted by one person into the care of another (Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains [2nd edition., Vol. 1, p. 463]. New York: United Bible Societies). Beyond the fact that they are both deposits I see no compelling reason to parallel v12 & v14.
It may be the writer is alluding that his reader should take as a good care of the deposit he has been given as God takes care of that which the writer has deposited with him.