Contamination depends on, how the bore well is constructed. If the bore well is provided with deep casing pipe and the static water level is much deeper and the gap between the bore well casing and annular space is grouted with clay or cement then the possibility is very very less or nil. If the annular space is not grouted, then slowly the water will percolate and reach the annular space and trickle down into the bore well. During rainy season the effect will be more.
Either your neighbour has to provide grouting in the well or you have to convert the second pit into a sump with 4 sides made of concrete and empty the water regularly with some local arrangement.
Contributor : A. Rajamohamed Ambalam (https://www.indiawaterportal.org/users/rajamohamed-ambalam )
This is a typical urban problem. Basically, the sump cannot get polluted by this if it is made of water tight construction in RCC or brickwork and in both cases duly plastered and is raised above the ground level. The borewell water in a bore of 350 feet deep cannot also get polluted by this water because the soil bacteria will purify the pollutants. The only objection will be that Bangalore being rocky, there can be crevices through which the polluted water can travel down, but then, here also the growth of bacteria in the crevices slowly grows further and becomes a "plug".
The most important issue is they can put the entire sewage into a septic tank and followed by an upflow filter and discharge the final effluent legally into the roadside drain. The only issue is whether their house basement level is high enough to permit the final effluent to flow by gravity into the roadside drain.
If not they have to pump it and store in an elevated tank from which the effluent has to go out at a mild uniform rate of flow through the day. Such an arrangement is easily made by inserting a hose inside the tank and typing its top end to a float and drilling a hole of some 15 mm in the flexible hose some 15 cm below the float.
Contributor : Dr. S. Sundaramoorthy