I agree that the intention is probably regarding the running of utilities through a park or someone coming in and erecting some sort of structure, like a fishing hut or party tent, concert grandstand or stage... in a park or on a beach etc. However, as loosly as it might be worded, to catch all possible issues, it has one key phrase that applies. "unless authorized by permit".
To me, that means, without bringing up the statute as you presented here. Simply go to whomever is of authority and get Permssion, (PERMIT) for your pourpose. Present your intent and show, if required, your tecnique for locating your finds and assurances that you won't do any harm.
I wouldn't raise the issue of the statute as, A.) it may not specifically apply to your situation or intentions and B.) it might confuse the situation making someone say NO, right off the bat. Some bureaucrats and government employees don't take risks very easy. They don't think independantly or make decisions, unless their decision is supported by policy or law. They rely heavilly on such things as policies or Statutes and if you present that to them, they might, even if irrelevant to your situation, try to apply it to you. If you get someone experienced you might be OK in that they will know that another ordinance applies to you. But, get someone with less experience and you might have trouble. That person might make you put up bond, fill out forms, or pay for permits.... Go before a city council or zoning or village board... By remaining vague, someone without experience will have to seek the guidance of someone of more experience. Not slamming government workers here. I just know from days working as a legal assistant, going to the county clerk to file a court document or to the sheriff to have a summons served or an eviction executed... Or going to the recorder of deeds or court clerks to get copies of files... they wouldn't do anything unless everything was done exactly to policy and written instructions or authorizations from someone higher then them.
The other option is to go ahead and do your business and plead ignorance if stopped. Say you thought that since it was a public park, and that you were only cutting little slits in the turf... Ask who to get permission from and Then go and get permission if demanded. If you are digging proper plugs, poking around with a probe or cutting a slit in the ground with a knife and pulling out a coin with your fingers, That might or might not qualify as "Excavation". If nobody notices that you were ever there, or you haven't left any holes or damaged any grass, aren't digging in flower beds..., and your activity isn't an obvious "Excavation", nobody may care. On the other hand, Pull up with a Ditchwitch and a truck load of building materials..., without a permit, and you might have a problem.
