Thanks.

It appears so. The smaller kokugos don't have it and the example in daijr/s is from the 13th century. I think it can be dropped.
Daijr agrees with obunsha that 転く only applies to to the "spin" sense. As 転めく is only in daijs and doesn't register in the n-grams, I think it can be hidden.

@@ -11,0 +12 @@
+<ke_inf>&sK;</ke_inf>
@@ -14,0 +16 @@
+<ke_inf>&sK;</ke_inf>
@@ -22 +24 @@
-<gloss>to be dizzy</gloss>
+<gloss>to feel dizzy</gloss>
@@ -28,6 +30 @@
-<gloss>to bustle about</gloss>
-</sense>
-<sense>
-<pos>&v5k;</pos>
-<pos>&vi;</pos>
-<s_inf>original meaning</s_inf>
+<s_inf>orig. meaning; also written as 転く</s_inf>

isn't it sense 2 that's archaic?

眩く is in a majority of refs and gets the most n-gram counts.

Several of the kokugos mention the くるくる回る sense. Maybe it would be better to have an "original meaning" note rather than an [arch] tag.

Google N-gram Corpus Counts
╭─ーーーーー─┬────────┬───────╮
│ 眩く　　　 │ 15,112 │ 91.0% │ - remove [io] tag (daijr, koj, meikyo, smk, etc.)
│ 眩めく　　 │    449 │  2.7% │ - (daijs, sankoku)
│ 転く　　　 │     22 │  0.1% │ - (obunsha: ①は、「転く」と書くことが多い。)
│ 転めく　　 │      0 │  0.0% │ - (daijs)
│ くるめく　 │  1,021 │  6.1% │
├─ーーーーー─┼────────┼───────┤
│ 眩いて　　 │    129 │ 71.3% │
│ 眩めいて　 │      0 │  0.0% │
│ 転いて　　 │      0 │  0.0% │
│ 転めいて　 │      0 │  0.0% │
│ くるめいて │     52 │ 28.7% │
├─ーーーーー─┼────────┼───────┤
│ 眩いた　　 │    224 │100.0% │
│ 眩めいた　 │      0 │  0.0% │
│ 転いた　　 │      0 │  0.0% │
│ 転めいた　 │      0 │  0.0% │
│ くるめいた │      0 │  0.0% │
╰─ーーーーー─┴────────┴───────╯

@@ -3,0 +4,3 @@
+<k_ele>
+<keb>眩く</keb>
+</k_ele>
@@ -8 +11 @@
-<keb>転めく</keb>
+<keb>転く</keb>
@@ -11,2 +14 @@
-<keb>眩く</keb>
-<ke_inf>&io;</ke_inf>
+<keb>転めく</keb>
@@ -17,8 +18,0 @@
-<sense>
-<pos>&v5k;</pos>
-<pos>&vi;</pos>
-<misc>&arch;</misc>
-<gloss>to spin</gloss>
-<gloss>to revolve</gloss>
-<gloss>to twirl</gloss>
-</sense>
@@ -35,0 +30,8 @@
+<sense>
+<pos>&v5k;</pos>
+<pos>&vi;</pos>
+<s_inf>original meaning</s_inf>
+<gloss>to spin</gloss>
+<gloss>to revolve</gloss>
+<gloss>to twirl</gloss>
+</sense>