I wanted to liquidate a particular position in my SEP account and reinvest the proceeds in another mutual fund to be held in the SEP. When I went to do so on the website of the trading company, there was a dropdown asking me to specify the "tax lot" method (FIFO, LIFO, etc). Am I mistaken in thinking that short-term/long-term capital gains issues do not apply to positions in a SEP account if the proceeds of the sale remain in the SEP?
You are correct in that short-term/long-term capital gains issues don't affect the tax treatment of the money coming out of the SEP account, and gains issues don't affect anything since you are trading between mutual funds held inside the SEP. But when you redeem some of the shares in a mutual fund, you can specify whether you want to redeem the most recently purchased shares (might be reinvested dividends and reinvested capital gains in the past few years) -- LIFO -- or the first purchased shares -- FIFO -- or something more specific (redeem 30 shares purchased on 02/21/2019 and 10.853 shares purchased on 12/21/2020 etc) if the fund allows it, or use the average share method (which many funds default to these days if you say nothing). If you keep track of your investments in money-management programs such as Quicken, you need to make appropriate entries so that your records match the trading houses's records. But, regardless of which choice you make as to which shares you sold, there are no tax consequences to your choice.