From the tone of his post (referring to the horizontal output tube as the "high voltage output tube", et al.) I'd guess the OP is very new to TV repair and probably should, IMO, leave any service work on his set to a qualified person. Television repair is much more involved than radio or audio servicing; moreover, the high voltages present in a TV set, especially around the CRT (picture tube), can be dangerous or lethal if not approached in the correct manner.
BTW, my best friend's parents' first TV was a split-chassis Philco console similar to the OP's. I never saw their set in operation (I think they retired it and got a new, smaller set when my best friend and I were very small kids, IIRC--I'll have to ask him if he remembers anything about it), but I do remember seeing the set in their garage many years ago. The set is long gone by now, as my friend's parents no longer live in the neighborhood (four houses down the street from where I grew up), but the OP's mention of his split-chassis Philco 21" set immediately rang a bell in my head and sent my mind reeling back at least thirty years.
Ah, memories.
I wonder how many of those split-chassis Philcos were made, in what year, and how reliable they were. Did they have a decent picture?
My best friend and I grew up in a far-suburban area for Cleveland TV and if I remember, there was a rather large antenna on the roof of his folks' house (the antenna was VHF only as Cleveland only had channels 3, 5 and 8 at the time, late '50s-early '60s).
Were the split-chassis Philcos' tuners sensitive enough for use in far-suburban to fringe areas? I'm not sure, but I think my friend's folks' set had a 6BQ7 or other type cascode RF amplifier tube in the tuner and at least three video IF stages. However, if it had a garden-variety RF amp tube such as a 6GK5, 6HA5 or other small-signal tube, I can see the need for a large antenna -- sets with this type of low-gain RF amp (compared to cascode RF stages) needed all the incoming signal they could get, especially in moderate to weak signal areas. I live in an area of northeastern Ohio which is located some 35 miles from Cleveland and at least 40 miles from most of the area's television transmitters; I bet there were a lot of TV sets around here in the '50s-'60s, Philcos and other makes, with cascode RF stages (to say nothing of large near-fringe-area antennas on rooftops, some of which are still standing but falling apart), as the TV signals here are nowhere near city grade, especially in these days of all-digital TV; in fact, they never were, even when TV was all analog (the entire village is wired for cable, and just about everyone here has it or satellite).