What is that “accelerator”? Does it have a name?

You might be mistaking rebroadcasting a transaction for accelerating? Both are completely different, and rebroadcasting never helps at all in such scenarios.

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The OP of that thread also uses other available free transaction accelerators like viaBTC and sometimes the transactions just get confirmed because the fee rates have dropped and not through his intervention.

From my experience none of the free accelerators found online work, expect for ViaBTC, but your tx fee is still too low to be accepted there. And other than ViaBTC and Binance paid accelerators there aren't any other reputable services you can try. Mempool accelerator seems trustworthy and offers lower prices but it seems like their service is still not running, it's been like that for months now.

Compared to current average fees, your fee is not very low and it's been already more than 24 hours since it was broadcasted. The fees are currently still getting higher during the day but they should start dropping after midnight, and I predict your transaction will get confirmed within the next 12-24 hours. From personal experience, even when using low fees, I've rarely had or seen transactions go unconfirmed more longer than 24-36 hours, unless using an extremely low fee(1-10sat/vB). So, unless this is an emergency, I would not worry about your transaction remaining unconfirmed for much longer.