They can be used for the same meaning. Therefore, I have to explain to clarify to you those two verbs.
but to understand these words, we need to be back to the origin of them.
أَغْمَضَ = أَ+غْ+مَ+ضَ ==== > غَ+مَ+ضَ
aghrmada is a verb originally comes from ghamada,
فعل زيد بألف على وزن أفْعل
غَمَض has the meaning of سَتَر، أخفى... So, the verb aghrmada will check the same meaning.
The second meaning of using aghrmada are: تَسَاهَل تغَاظَى تَسَامَحَ
مثال ذلك:
أغمضتُ عما قاله في حقي من كذب.
في القرآن الكريم: "ولا تيمموا الخبيث منه تنفقون وَلَسْتُمْ بِآخِذِيهِ إِلاّ أَنْ تُغْمِضُوا فِيهِ" من سورة البقرة
غَمَّضَ a verb coming from غَمَضَ the same verb.
فعل زيد بتضعيف عينه
على وزن فعَعْلَ
has the same meaning of ghamada. The other meanings of it are: أَبْهَمَ أغمضَ
مثال
غَمَّضْتُ عَمَّا سَلَف
غَمَّضَ كلامه علي
for your expression: We can use the both in a normal way, it's not a problem.
In literature, they haven't the same meaning.
أَغْمَضْتُ عَيْني = I close my eyes.
غَمَّضْتُ عَيْنَيْ = I close my eyes (because it's not good to see) غَضُّ البَصَر