https://ja.hinative.com/questions/16556698
  "However, in novels and the like, it is often to write 「凝視める」and It is read 「みつめる」. Because「凝視」 is a difficult say way of 「見つめること」 so the sentence become formal and poetic."

〈見詰／見つ／みつ／瞶／凝視／見凝〉める

Google N-gram Corpus Counts
╭─ーーーー─┬───────────┬───────╮
│ 見つめる │ 1,301,812 │ 92.0% │
│ 見詰める │    26,704 │  1.9% │ - rK (kokugos)
│ 凝視める │       364 │  0.0% │ - add, sK
│ 瞶める　 │       212 │  0.0% │ - [iK] to [sK]
│ 見凝める │        38 │  0.0% │ - add, sK (Robin's comment below)
│ みつめる │    85,644 │  6.1% │
├─ーーーー─┼───────────┼───────┤
│ 見つめて │ 1,387,754 │ 86.2% │
│ 見詰めて │    41,742 │  2.6% │
│ 瞶めて　 │       626 │  0.0% │
│ 凝視めて │       537 │  0.0% │
│ 見凝めて │        53 │  0.0% │
│ みつめて │   179,814 │ 11.2% │
╰─ーーーー─┴───────────┴───────╯

@@ -11,0 +12,5 @@
+<ke_inf>&rK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>凝視める</keb>
+<ke_inf>&sK;</ke_inf>
@@ -15 +20,5 @@
-<ke_inf>&iK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>見凝める</keb>
+<ke_inf>&sK;</ke_inf>

I'd support that.

@@ -15 +15 @@
-<ke_inf>&rK;</ke_inf>
+<ke_inf>&iK;</ke_inf>

凝める isn't in my refs and I don't know where it came from. Possibly a mistyping of 見凝める, which gets a handful of hits in Aozora.
Shouldn't 瞶める be iK?

@@ -17,4 +16,0 @@
-<k_ele>
-<keb>凝める</keb>
-<ke_inf>&oK;</ke_inf>
-</k_ele>
@@ -30,3 +26,3 @@
-<gloss>to stare at</gloss>
-<gloss>to gaze at</gloss>
-<gloss>to look hard at</gloss>
+<gloss>to stare (at)</gloss>
+<gloss>to gaze (at)</gloss>
+<gloss>to look hard (at)</gloss>
@@ -34 +30 @@
-<gloss>to fix one's eyes on</gloss>
+<gloss>to fix one's eyes (on)</gloss>