Thin white horizontal line across otherwise black screen

Hello,

CAUTION: To prevent damage to the CRT phosphors, immediately turn down the brightness so the line is just barely visible. If the user controls do not have enough range, you will have to locate and adjust the master brightness or screen/G2 pots.

A single horizontal line means that you have lost vertical deflection. High voltage is most likely fine since there is something on the screen.

This could be due to:

Dirty service switch contacts. There is often a small switch located inside on the main board or perhaps accessible from the back. This is used during setup to set the color background levels. (On some sets, this is located on the CRT neck board and may be a jumper plug or other means of selecting service mode - not an actual switch.)

When moved to the 'service' position, it kills vertical deflection and video to the CRT. If the switch somehow changed position or got dirty or corroded contacts, you will have this symptom. Flip the switch back and forth a couple of times. If there is some change, then replace, clean, resolder, or even bypass it as appropriate.

Bad connection to deflection yoke or other parts in vertical output circuit. Bad connections are common in TVs and monitors. Check around the pins of large components like transformers, power transistors and resistors, or connectors for hairline cracks in the solder. Reseat internal connectors. Check particularly around the connector to the deflection yoke on the CRT.

Bad vertical deflection IC or transistor. You will probably need the service manual for this and the following. However, if the vertical deflection is done with an IC, the ECG Semiconductor Master Substitution guide may have its pinout which may be enough to test it with a scope.

Other bad parts in vertical deflection circuit though there are not that many parts that would kill the deflection entirely.

Loss of power to vertical deflection circuits. Check for blown fusable resistors/fuses and bad connections.

Loss of vertical oscillator or vertical drive signals.

The most likely possibilities are in the deflection output stage or bad connections to the yoke.
Hope it works well...