A logic probe would be helpful.
Here is a thought: After putting the game in lamp test, try unplugging the two connectors on the right side of the MPU board (Cabinet and Playfield Switch matrix) and see if your light problems change???
The data is repeatedly being updated and clocked into the latches. Which requires not only tying the 4 data lines high or low, but also the 4 address bits that address one of the 16 latches inside the MC14514's. So, in my mind, its not really worth trying to do this. I find it easier to simply probe the lines from start to finish.
If you can find some common-ality to all the lights that don't work (won't light or stuck on all the time), then you might be able to narrow it down to just one of 4 data or 4 address lines. Once you have done that, then its a matter of checking continuity from where it starts (Pin on PIA in MPU) to where it ends up (Data inputs on ICs). Taking into account any resistors that are used between the ICs and the output pins on the connectors. Beep test is not as good as actually reading the ohms value and possibly comparing it to one of the same types of signals that you know is getting through (another data line). Again, a logic probe makes this kind of troubleshooting much easier since you can see highs, lows, pulses and possibly floating lines. A DVM is not really very useful in this case. Of course, an Oscilloscope is much better.
You will see that PA5-PA7 from PIA U10 become PD0, PD1, PD2 and PD3 (lamp data) at J1. PA5,6, and 7 are also used to select the dipswitch banks. They go to J4 on the lamp driver board. And then feed each of the 4 Latches as "I" at pin 23. The Desired output is selected (addressed) in all 4 Latches via AD0-AD3. These start out at U10 as PA0 - PA3. Which are also used for Playfield switch matrix output strobes. Which is why I suggested unplugging the cabinet and playfield matrix above after putting the game in lamp test. A grounded switch strobe at the coin door or on the playfield can hold a Lamp Address strobe low causing issues. This sometimes shows up as a Slam Switch weight touching the coin door (no more mylar insulator sticker) or a stuck coin switch.
You will note on the Lamp Driver board, the Data and Address lines have series resistors R71 through R79 which are 20K which is why you can't use continuity (Beep) test. So you pretty much have to start out at the 6821 PIA (U10) pins and ohm them out to the male header pins (taking into account the 1.2K resistors used in series with the output as part of a resistor/capacitor filter. Then, from the resistors or back side of the board male pins to the back side of the board to male pins on the Lamp driver board (pretty close to zero ohms for all since it is direct connect wiring). Then, from the male pins into the lamp driver board (again, through 20K resistors) ending up at the pins of each IC.
There is also a page in the manual/schematics that show you the wire connection from one board to the other. The one attached here is from Space Invaders.