The part "my drift" means there is a chain of thoughts or an inside meaning that is not clearly defined. the expression is used whenever you think the listener may be confused or not follow your main idea.
The origin of the word "drift", according to OED, was in the 1520s:
drift (n.) Sense of "what one is getting at" is from 1520s. Related: Drifted; drifting.
I can't know for sure the origin of the expression "if you catch my drift".
Meaning
See you in the funny paper[s] means "Goodbye, see you soon".
A Dictionary of Catch Phrases (1986) by Eric Partridge and Paul Beale says:
see you in the funny papers (—often and orig. I'll). 'This jocular farewell suggests that the person addressed is rather laughable: US: 1920s; extinct by the 1950s' (R.C., 1978). Perhaps adopted in the UK from American servicemen c. 1943. By c. 1955, (I'll) see you in the funnies.
Etymology
The OED has funny paper from 1874 and funny column from 1860, meaning "a (section of a) newspaper containing humorous matter or illustrations".
1920
The earliest example I found of the phrase is in a letter in Commercial Telegraphers' Journal (August 1920, Vol. XVIII, No. 8):
So long, boys, see you in the funny paper. "30."
J. N. HANNA,
Box 1004.
1921
Another in the Union Postal Clerk (March 1921, Vol. XCII, No. 3):
We will see you in the "funny paper" next month.
PRESS COMMITTEE.
1921
Here's a April 15, 1921 letter published in University of Virginia student paper The Virginia Reel (April 18, 1921 Vol. 1, No. 8):
Well, boys, must close now. La, la, till the next time, and I'll see you in the funny papers. Ever your, ADELAIDE.
1922
Here's a 1922 example in the signoff of a report in The Tusla Scout from Troop 12 by Ed M'Lain (published in The Tulsa Daily World, March 19, 1922):
Good-bye, see you in the funny paper.
This use by scouts suggests it's not insulting, but may be used in a good-natured, light-hearted mocking manner.
Best Answer
This expression did not originate with television. It has a much longer history, dating possibly to the 17th century. From Wikipedia:
As you can see, Andrew Jackson used the expression in 1829, which was well before television and even radio.
This Google NGram supports the contention that the phrase has existed for a long, long time: