It depends on your architecture. See the Masa diagrams - https://community.splunk.com/t5/Getting-Data-In/Diagrams-of-how-indexing-works-in-the-Splunk-platform-the-Masa/m-p/590774 The index-time settings (line breaking, timestamp extraction indexed fields extraction and the such) are applied on first "heavy" (based on a full Splunk Enterprise installation, not UF) component in event's path. So if your ingestion process is UF->idx you need TAs on indexers. If you have TA with modular inputs on HF, the same HF will do the parsing stuff so for data coming from this HF you will need index-time settings in a TA there and search-time settings on SH. If you have a fairly complicated (and very unusual but I can think of a scenario where it could be used) scenario like UF1->HF1->UF2->HF2->idx you need index-time settings on HF1 since it's the first heavy component. It does the parsing and sends the data down as parsed so subsequent components don't need to parse the data.
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