Tami Shimoni is an agent with Gag.
Pappa Barzilai is a spymaster with Gag.
First some information, scant though it is, on Gag. It is used a time or two in all caps but mostly in blurbs about the adventures. In the stories themselves, it is usually with lower-case though the first G is often capitalized. The reason for the discrepancy can be blamed on the fact that just about no one in the private sector knew anything about it at all and those that did largely just knew rumors. Even those in the various intelligence groups in Israel had sketchy information on it.
What is known by some is that "thee was a roof organization of the vaious security services, including military, the Shin Bet - already exotic in its own secretive right - and other branches of the police. In Hebrew the word for 'roof' was 'gag'. The organization was known, informally, and even against regulations (for it should have no name) as Gag." What that means is that for the power and authority that the various bureaus had, there was something above them that could, if it felt needed, override orders and take charge. We learn largely anecdotally that it does not often press its leverage but when it does, it means it.
Back to Shimoni, though, it is important to note that while he is an agent with Gag and he has several recorded adventures in that capacity, he is in truth only a part-time operative. When needed, he is called and he shows up without fail. When not needed, he is a Detective Inspector with the Tel Aviv police and has been for more than a few years. He enjoys his work tremendously and would gladly stay doing it and not stepping in the shadowy world of Gag except his devotion to his country does not allow him to refuse requests for assistance.
Those requests come from Pappa Barzilai who, if anyone asked (no one really did), was some sort of functionary doing something mundane and basically unintelligible at the port of Tel Avia, a glorified clerk at best and by and large a pleasant older man who should have retired a few years back but obviously could not afford to. Even Mama Barzilai would tell you that because that sweet grandmotherly old lady truly believed it. Mind you, Pappa did not lie to Mama about his job. He just never saw the need to bother letting her know the truth.
Now comes the one fun fact about the relationship between Shimoni and Barzilai. Ever since Shimoni graduated from the police academy, he roomed with the Barzilai's. Their previous tenant had been a policeman, too. Shimoni enjoyed living with the Barzilai family because it was very much a family setting and the rent was cheap and Shimoni did not make all that much even as an Inspector. And for the several years he had been with them already, he, too, never once though the rather short and very rotund older man was nothing more than what he let everyone believe. True, Shimoni would note that Barzilai would disappear at the oddest times for one mix-up or another at the port but the older man was so blasé and unassuming, it never occurred to Shimoni to think anything else.
Which is a factor that will always keep Shimoni humbled when he considered his true and considerable skills as a detective; that he could live in the Barzilai household for so long and have nary a clue.
It would be a police matter that would extend into the cloak and dagger world that bring Shimoni into the fold of Gag and the knowledge that the chubby sweet old man was really a brilliant, cold-as-ice, spymaster. And it would other police situations which would get him recalled to Gag duty. And the knowledge that what he should be doing as a police officer, sworn to obey the laws and regulations of the land, would often conflict with the demands of his duties with Gag where only results mattered.