This is very easy to diagnose on your board. Thing is, even if all traces read 0 ohms between where they go, doesn't rule out that this particular signal isn't affected by the corrosion between that signal and another close by. Continuity only tells you there is a direct connection between those 2 points, but it won't show you that the same wire might be reading a weird resistance between another pin that isn't related at all and is affecting the signal.
Is U1 on a socket now that it has been replaced ? I hope so, rule of thumb if you replace an IC , you should put a socket instead. If it's socketed , pull out the chip , bend pin 19 and put the IC back in. Is the string still dimly light ? If so (very probable) it means that R8 is sensing a voltage on it's pin and that is what is driving the lights. If this is the case , it means that corrosion is still present on that trace and you now have to find out where on the board that trace is affected. Since pin 19 (signal) and pin 20 (VCC) are so close, it sounds very likely that you still have corrosion affecting pin 19 and creating a resistance to pin 20 , which is in turn sending voltage to R8 and lighting up the string. If you measure resistance between pin 20 and pins 2,5,6,9,12,15,16 and 19 they should all be very similar, I'm almost certain you'll measure a resistance between that differs from the rest between pins 20 and 19.
The overall troubleshooting sequence should be this : Under similar conditions , compare the voltage (DC volts , black probe on ground) and resistors R8,R11,R14,R17 and R20. They are supposed to have a voltage very close to each other. If this is the case, then the trouble would have to be on the side towards the transistor/triac and the bulbs. If the voltage of the problematic line differs from the other , then you have to look at the other side of the circuit , which is the IC directly. If it's on the IC side , then you have to compare the voltage of each input D0 to D7 to check if they are similar or not. If they are (they should) then you've identified the problem between the output of the IC and resistor R8.
You said that the lights have all their levels of dimming , which means the side with the transistor and the triac are "functionning". That still doesn't rule out if corrosion is in that part of the circuit.
Are you confident enough in your work to actually show us a picture of the U1 area properly cleaned and repair after the corrosion ?
On the picture , compare what's marked in orange first, then the side in red of the IC , and last the green zone that drives the triac.
pin6.png