The reason why excavations of the Villa of the papyrii in Herculaneum had to end is usually cited to be "gas invading the tunnels". That is a common problem in coal mining. However, volcanic deposits, unlike coal, do not release toxic gas. What kind of gas is this referring to?
If we look at the book Buried Herculaneum, By Ethel Ross Barker (1908) we find on page 18 a discussion of these excavations:
To the actual physical difficulties of the work was added great discomfort from the cold dark and damp and from occasional exhalations of poisonous gases especially of carbonic acid gas and sulphuretted hydrogen during the excavations on the Villa.
The terminology is 1908, but seems to mesh up with what is expected in volcanic caves. Hydrogen and Sulfur gases and carbon dioxide type compounds. Looking at the PDF Hazards of Volcanic Gases Table 57.1 lists Carbon Dioxide, Sulfur Dioxide and Hydrogen Sulfide as dangers in volcanic cave environments.
Note that there are major differences between the characteristics of the flows received by the cities of Pompeii and Herculaneum. From a PBS page
Pompeii, lying to the east and south of the mountain, was buried under approximately 40 feet of fine ash. Deadly at the time, this layer of ash was relatively easy to excavate seventeen centuries later when the city was rediscovered. Herculaneum, on the other hand, lying to the west of Vesuvius, experience its full fury with a hot thermal blast, poisonous gasses, and a flow of molten volcanic mud that, when cooled, buried the remains under an 80 foot deep bed with the density of concrete. For this reason Herculaneum has been much more difficult to excavate, and some areas of the city have remained inaccessible due to pockets of trapped gas.
So this article seems to equate the gases with those of volcanic origin as well.