If one should not use a little roofing cement around a chimney to cure a leak that doe snot mean lots of roofing cement will be helpful at all. Due to the temporary nature of this repair one must assume further problems, hazards and damages will be occurring. Large amounts of roofing cement may rips and cracks more likely to occur. Excessive patching like this is also an indication leaking keeps occurring again after the last ineffective repair.
Usually the real cure is to have the entire skylight and roof shingles around it pulled out by a roofing contractor and to pay to have the existing skylight reset. This will be expensive and may not be a cure for the problem.
PRIOR to expiration of your home inspection contingency further evaluation of the existing conditions by a roofing contractor is necessary to determine the scope and cost of the necessary repairs and hazards.