It is going to be difficult to diagnose:
1. While the DACs are exposed on the storage board for easy access, they have current outputs so there is nothing to probe except the voltage reference. Note that since the vertical works, the shared voltage reference and dividers must be correct.
2. The vector generator board, which has all of the interesting signals to probe, is hidden below the storage board and difficult to access.
If I was to make a guess, it is that U6402, a CA3046 transistor array, on the vector generator board is bad. This transistor array converts a single ended voltage output from the vector generator to differential current outputs for the horizontal signal. Historically these transistor arrays seem to be the most unreliable ICs.
The other likely option is a resistor which has increased in value, and it is certainly worth probing all of the resistors in the signal path to see if any are high.
That leaves the 4053 multiplexer, which is another IC with high failure rate.
Given the difficulty in diagnosing it, except for checking the resistors, I would probably shotgun replace all of the ICs including the DAC.