タメぐちをきく	22	1.1%
タメ口をきく	1156	59.1%
タメ口を聞く	339	17.3%
ためぐちをきく	25	1.3%
ため口をきく	325	16.6%
ため口を聞く	90	4.6%

@@ -11,0 +12 @@
+<ke_inf>&sK;</ke_inf>
@@ -14,0 +16 @@
+<ke_inf>&sK;</ke_inf>
@@ -18,7 +19,0 @@
-<re_restr>タメ口をきく</re_restr>
-<re_restr>タメ口を聞く</re_restr>
-</r_ele>
-<r_ele>
-<reb>ためぐちをきく</reb>
-<re_restr>ため口をきく</re_restr>
-<re_restr>ため口を聞く</re_restr>
@@ -29 +24 @@
-<xref type="see" seq="2021640">タメ口・タメぐち</xref>
+<xref type="see" seq="2021640">タメ口</xref>

GG5: ため口をきく speak in one's peer language (to sb who is not a peer).
ため口をきく	325
タメ口をきく	1156
ため口を聞く	90
タメ口を聞く	339

MeCab indicated 聞く.

@@ -3,0 +4,6 @@
+<k_ele>
+<keb>タメ口をきく</keb>
+</k_ele>
+<k_ele>
+<keb>タメ口を聞く</keb>
+</k_ele>
@@ -8 +14 @@
-<keb>タメ口をきく</keb>
+<keb>ため口を聞く</keb>
@@ -10,0 +17,5 @@
+<reb>タメぐちをきく</reb>
+<re_restr>タメ口をきく</re_restr>
+<re_restr>タメ口を聞く</re_restr>
+</r_ele>
+<r_ele>
@@ -11,0 +23,2 @@
+<re_restr>ため口をきく</re_restr>
+<re_restr>ため口を聞く</re_restr>
@@ -15,2 +28,4 @@
-<gloss>to talk unreservedly</gloss>
-<gloss>to not use polite language (desu-masu) even when one should</gloss>
+<pos>&v5k;</pos>
+<xref type="see" seq="2021640">タメ口・タメぐち</xref>
+<gloss>to talk casually</gloss>
+<gloss>to use one's peer language (to others)</gloss>

I understand きく is the verb used with the word ため口
Daijisen for example uses ため口をきく to illustrate
It probably derives from 口をきく

I don't know if it has a kanji