I don't think it does imply a lack of ambiguity, but in case it helps I've made the glosses a bit broader.

@@ -13,0 +14 @@
+<gloss>to open up to someone else</gloss>
@@ -15,2 +16 @@
-<gloss>to open one's heart</gloss>
-<gloss>to open up to someone else</gloss>
+<gloss>to be openhearted</gloss>

Second google hit for "心を開く方法":
心を閉ざしている人の心を開く方法12選！ 心を開けない人 

Another Example: 7 rules of listening and speaking to get others to open up to you: 
相手に心を開かせる聞き方と話し方・７つの法則
https://next.rikunabi.com/journal/20160711_1/
Text includes: 心を開きにくくなることもあります   <--- sometimes it might get hard to open their hearts
『初対面で相手の心を開く！46のルール』             <--- open your interlocutor's heart at your first meeting! 46 rules
Google mistranslates these both backwards, ie.: "Open your heart to someone when you meet them for the first time! 46 rules"

相手の心を開く	702	 <-- open someone else's heart
相手の心を開かせる 566    <-- get someone else's heart to open 

is higher than, for example:
自分の心を開く	613	  
私の心を開く	51

Thank you for the feedback on eijiro.  I know I see questionable errors there all the time.  It's true, if eijiro agrees with the specific real-world encounter I'm looking at, I tend not to triple-check, and sometimes I should.  I did concede there isn't *actually* a second sense, this is more of a pragmatic suggestion.  For example, without context, what does this mean:

心を開く方法

The current glosses suggest this is unambiguous. It's your own heart. English speakers have no intuition that there are two opposing interpretations of this phrase. A second sense would make this clear.

This ordering seems more common than our intuitions would suggest.  If you search *just* google news for just for the string "相手の心を開く" there are 18 pages of actual results.  regular google yields an infinite scroll.

My suggested [2] is the form I encountered it in the wild, so I have a bias.  All I can say is that I believe a sense[2], or some other way in sense[1] to suggest the ambiguity, would be helpful to learners.

I'm not seeing two senses here; more a broad use of the expression.
Be wary of too much reliance on Eijiro. We warn against it in the editorial policy page. It's OK for confirmation.

@@ -14 +13,0 @@
-<s_inf>自分の～</s_inf>
@@ -18,8 +16,0 @@
-</sense>
-<sense>
-<pos>&exp;</pos>
-<pos>&v5k;</pos>
-<misc>&id;</misc>
-<s_inf>他人の～</s_inf>
-<gloss>to get someone to open up to you</gloss>
-<gloss>to unlock someone's heart</gloss>

We don't usually do notes like I've added, but maybe you can think of something to clarify explicitly

@@ -13,0 +14 @@
+<s_inf>自分の～</s_inf>
@@ -21,0 +23 @@
+<s_inf>他人の～</s_inf>

https://eow.alc.co.jp/search?q=心を開く
（人）の心を開く秘訣
key to unlocking someone's heart
内気な（人）の心を開く
draw someone out of his shyness
人々の心を開く
open people's minds
open the minds of the people

[1] looks like something you do to your own heart, and that's correct.  But you can also 開く someone else's heart in Japanese, which is not something you can readily do in English.  If I say "open up someone else's heart", that sounds to me like surgery.

Case-in-point, see how this translator reverses the structure for an English audience:
(Context: running errands for stubborn old woman before she will help them): 頑張っておばあさんの心を開こうか 
Let's do what we can to get her to open up to us

While these are obviously variants of the same sense, I think doing this as one sense in English would be confusing.

Eijiro has some other potential glosses for other people's hearts that you might be interested in glossing over.

@@ -15,0 +16,8 @@
+<gloss>to open up to someone else</gloss>
+</sense>
+<sense>
+<pos>&exp;</pos>
+<pos>&v5k;</pos>
+<misc>&id;</misc>
+<gloss>to get someone to open up to you</gloss>
+<gloss>to unlock someone's heart</gloss>