I am sorry about it, but I simply have to write this answer.
Probably the reason for your confusion is that you have a very good intuition in languages. The problem here is not whether to choose заискивающий or заискивающийся, but with the choice of the word itself and, which is more important, the government.
OK. If you leave the word заискивающий in your poem, then it needs to be followed by preposition перед and the word must be in Instrumental. It should look like this:
мне теперь не до твоего смол-тока,
перед японским пивом заискивающего.
Actually here the usage is not quite correct, too: one can be ingratiating oneself with somebody, not something.
However, the other problem is that this word doesn't correspond with your desired translation. Заискивающий (перед кем-то) means ingratiating oneself (with somebody). For reference you can browse Academica, where you can find extracts from different dictionaries.
What could have caused the wrong usage of заискивать? Maybe this word resembles the word заикаться о ( заикнуться о), which means yпоминать вскользь, осторожно, намёками and could be used in your case, but it is very different in terms of stylistics, and I personally wouldn't use it here (it seems that the customs worker is quite enthusiastic about Japanese beer and talks about it continuously). Just remember the phrase
The reference to this word : (http://dic.academic.ru/searchall.php?SWord=заикаться)
I'll be adding my ideas of how those two lines could be translated here.
So far I have come up with some simplified versions (i.e. they are shorter than the original):
мне теперь не до твоего смол-тока (about what?)
о (всех - optional) прелестях пива японского
о японцах с их пивом (add suitable beer characteristics here)
Both of them show that the traveler is ironic about both the beer and the customs worker's enthusiasm. However, here the obsequiousness of the small talk is not directly mentioned.